For now, many of the world’s major central banks have moved decisively against inflation with a series of recent decisions to tighten monetary policy. But with past economic models of little use in the current environment, they are navigating without a clear road map.

“We’re definitely facing a very complex and uncertain environment,” said Klaas Knot, a policy maker at the European Central Bank and governor of the Dutch central bank.

The war in Ukraine is likely to shave more than 1 percentage point from global economic growth this year, while also pushing up inflation by a further 2.5 percentage points across the world, according to an estimate last week by the Organization for Economic Cooperation and Development.

“Central banks need to act on inflation, but what do they do [about] the slowdown? This is a poisoned chalice,” said Panicos Demetriades, a former ECB policy maker. “They can’t do both.”

The Federal Reserve raised interest rates by a quarter point on Wednesday and penciled in six more increases by year’s end—its most aggressive pace in more than 15 years—after U.S. inflation hit a 40-year high of 7.9% in February.

Fed Chair Jerome Powell told U.S. senators this month that he is ready to do what it takes to bring inflation down, and to follow the example of his predecessor Paul Volcker, who increased interest rates to 20% in 1981, triggering a recession and double-digit unemployment.

Still, at a news conference Wednesday, Mr. Powell said he hoped to lower inflation by taking the heat out of wage growth while also keeping unemployment low.

Some investors doubt that the Fed will be prepared to act aggressively to slash inflation.

“We think once inflation starts to come off the boil…the Fed eventually will opt to live with somewhat higher inflation than the 2% objective rather than forcing inflation down to 2% potentially at high cost in terms of activity and the labor market,” said Elga Bartsch, head of economic and markets research at BlackRock.

Out of 16 episodes since the late 1970s when central banks increased interest rates in the U.S., the U.K. and the eurozone, 13 ended in recession, according to Neil Shearing, chief economist at Capital Economics.

The Bank of England raised its key interest rate for the third time in as many policy meetings on Thursday, saying inflation could rise above 8% by year’s end, but it also softened its language on future rate increases. Earlier this month, the ECB unexpectedly said it could end its longstanding bond-buying program by September, opening the way for the first increase in its key rate since 2011, and roiling financial markets.

Policy makers in Europe are facing an especially difficult choice, given the rapid deterioration of the European economic situation, the continent’s geographical proximity to the war and its heavy reliance on ever more expensive energy—much of it from Russia.

The recent surge in European energy prices has pushed the region’s energy burden as a percentage of gross domestic product above levels reached in the early 1970s, whereas the U.S. is still well below that point, according to calculations by BlackRock.

In February, eurozone inflation was 5.9% in February, almost three times the ECB’s target rate of 2%.

The recent economic shocks have raised the risk that companies and consumers expect inflation to stay high, Mr. Knot said, potentially feeding a self-reinforcing price spiral, as businesses set higher prices and workers demand increased wages to compensate.

“Especially in these circumstances, it is important as a central bank to not add to the existing uncertainty, but to be a predictable actor and to be clear about our commitment” to returning inflation to target, Mr. Knot said.

Other central bankers are more worried about the slowdown of a eurozone economy that had yet to recover from the Covid-19 pandemic.

Yannis Stournaras, an ECB policy maker and governor of Greece’s central bank, said the war in Ukraine would push up inflation in the short term, but also reduce economic activity and thereby weigh on inflation in the medium term. “These competing forces create a wider range of risks than usual about our inflation projections,” Mr. Stournaras said.

“There is no playbook for central banks,” said Katharine Neiss, a former Bank of England economist now at PGIM Fixed Income in London. “I worry about low growth in Europe against the backdrop of high inflation, a stagflationary scenario…The ECB lost a bit of control of the inflation narrative.”

Central banks have been repeatedly surprised by the surge in inflation, contrary to predictions that it would fall back. At their Feb. 2-3 meeting, ECB policy makers debated recent errors in the bank’s staff economic forecasts and whether to put more weight on their own judgment and surveys, according to the minutes of the meeting.

“Given the current extreme uncertainty, it is wise to have an open mind and see how things unfold,” said Robert Holzmann, an ECB policy maker and governor of Austria’s central bank. He said he considered it important to return to a more neutral monetary-policy stance and higher interest rates, but said the bank must proceed “step by step.”

Central banks in South Korea, New Zealand and Singapore have already begun raising interest rates to stem inflation and have signaled more tightening lies ahead. Australia’s central bank held fire in March, but investors expect it to also begin raising borrowing costs within months. Hong Kong’s Monetary Authority raised its benchmark interest rate Thursday to maintain its currency peg to the U.S. dollar. Taiwan’s central bank raised its benchmark interest rate last week in response to robust growth, mounting inflationary pressure and the move by the Fed.

Other central banks in Asia might be nudged into tightening policy even as their economies weaken. The Philippines and India are struggling with accelerating inflation and a gloomier prognosis for growth. Thailand is facing rising inflation just as the tourism revenues that might have been expected from visitors from Russia and China have evaporated.

In India, inflation has been above the 6% upper bound of the central bank’s target range for two months straight and growth has slowed. For now, Indian central bank officials say they are more focused on the risks to growth than on inflation.

War, sanctions and the risk of financial-market turmoil means “the global economy is being dragged to the edge of a precipice,” Michael Debabrata Patra, deputy governor of the Reserve Bank of India, said in a speech earlier this month.

But elsewhere in Asia, central banks feel less pressure to raise rates. Policy makers in China and Japan, for instance, Asia’s two largest economies, aren’t expected to follow the Fed in tightening policy soon. Domestic inflationary pressures in both economies are muted, meaning the hit from higher commodity prices will be felt more forcefully on growth than on inflation, giving the People’s Bank of China and the Bank of Japan leeway to keep policy loose to support growth.

Write to Tom Fairless at tom.fairless@wsj.com