This comes on the heels of Friday’s jobs report, which showed the unemployment rate slipping to 3.9% last month, and average hourly earnings up 4.7%. The Federal Reserve is getting ready to raise rates as soon as March, and the combination of rising inflation and a tightening labor market is giving it cause to.

What the Fed doesn’t want to see is an environment where wage increases are pushing prices significantly higher, while a tight labor market and expectations of higher inflation are leading workers to command outsize wage increases. That could lead to inflation remaining well above the central bank’s 2% target, forcing it to raise rates sharply, and risk a recession.

To a degree, the rise in inflation over the past year reflects a rebound from the early stages of the pandemic, when prices cooled significantly. Even so, core prices have risen at a 3.3% annual rate over the past two years, which is the fastest pace since June 1993.

That pickup is entirely the result of increased goods prices, while service price gains have been muted. Core goods prices have risen at a 6.1% annual rate over the past two years, the most since March 1983. Core services prices have risen at a 2.6% rate over the past two years, which is lower than during the two years before the pandemic.

Goods—particularly big-ticket items such as cars and appliances—have been where supply problems have been the most pronounced. Goods have also been at the receiving end of the demand shift the pandemic brought on: Unable or unwilling to spend money on services such as airline tickets, Americans bought more stuff instead.

Rising wages have surely put some upward pressure on prices, too, but thus far they are largely secondary. If the pandemic loosens its grip, helping to alleviate supply-chain problems while provoking a shift in spending back toward services, inflation will cool.

How much it will cool is the big question. Rising labor costs could put a floor on how much price gains can moderate. A lot will depend on whether more people return to the labor market after the Omicron-driven surge in Covid-19 cases ends, easing hiring strains. And a lot will depend on how successful companies will be in passing rising labor costs on to their customers.

The tight job market and high inflation might not be feeding one another now, but that doesn’t mean they won’t in the future.

Write to Justin Lahart at justin.lahart@wsj.com