Read more: How to protect your savings against inflation

In a more extreme scenario, Apollo Global's Torsten Sløk estimated that if oil prices were to climb by $50 per barrel, second quarter inflation would be likely to increase by one percentage point, or 100 bps, above baseline. (Disclosure: Yahoo is a portfolio company of funds managed by affiliates of Apollo Global Management.)

"The events dovetail into an existing fear in the markets that inflation, at least in the States, could be quite sticky," Capital analyst Kyle Rodda said in emailed commentary.

Fed Chair Jerome Powell speaks during a press conference following a two-day meeting of the Federal Open Market Committee (FOMC) in January. (Reuters/Jonathan Ernst)

The key risk is that energy prices stay elevated long enough to affect consumer expectations, creating broader second-round effects and complicating the Fed's easing calculus, analysts said. The two-year Treasury break-even rate — a market measure of inflation expectations — has climbed to roughly 2.9% from around 2.3% earlier this year, according to Oxford Economics lead analyst John Canavan.

In comments on Tuesday, New York Federal Reserve president John Williams said the conflict in Iran could impact the outlook for inflation and raise uncertainty for the economic outlook.

"[Energy price increases are] something that would obviously affect kind of a nearer-term inflation outlook," Williams said. "We'll have to see how persistent this is and how long this is, but it would have an effect on overall inflation.”

Similarly, Minneapolis Fed president Neel Kashkari said on Tuesday that he was no longer as confident in his previous call for one quarter-point cut this year, noting that "with the geopolitical events, we need to get a lot more data in."

Traders are in near-consensus that the Fed will maintain its target rate of 3.5% to 3.75% at the upcoming March meeting, but predictions have strengthened that rates will remain untouched through June.

Historically, the Fed has tended to look past temporary supply shocks, particularly when they primarily affect headline inflation. But if energy-driven price pressures persist and begin feeding into core measures or inflation expectations, policymakers may find it harder to justify cutting rates in the near term.

For now, most baseline forecasts assume disruptions are short-lived, especially as US growth remains relatively resilient. But the longer crude prices remain elevated, the more difficult it becomes for the Federal Reserve to argue that inflation risks are firmly behind it.

"While the terms of trade shock on the US from higher oil prices might be small for the US as a net producer of oil, we caution that the US can still suffer beyond a single quarter if the consumer acts on perceived fears of higher prices and lowered real incomes," Wizman said.

Jake Conley is a breaking news reporter covering US equities for Yahoo Finance. Follow him on X at @byjakeconley or email him at jake.conley@yahooinc.com.