While that’s good for American households finally starting to see their inflation-adjusted earnings rise, it also deepens the puzzle for the Federal Reserve as officials weigh how much to raise interest rates in the months ahead. Low unemployment calls for more rate increases, but slow inflation doesn’t.

The consumer-price index, which measures what Americans pay for everything from hair spray to hotel room service, rose 0.1% in September after rising a seasonally adjusted 0.2% in August, the Labor Department said Thursday. September’s slight increase undershot economists’ expectations of a 0.2% rise.

In the 12 months through September, overall prices rose 2.3%, the smallest year-over-year change since February and down sharply from the near-3% year-over-year increases seen this summer. Excluding the more volatile food and energy components, core prices were up 2.2% on the year in September, the same rate as in August.

Two consecutive months of 0.1% increases in inflation “show the economic seas are calm when it comes to inflation despite the hurricane of selling hitting the world stock markets,” said Chris Rupkey, chief financial economist at MUFG Union Bank.

September’s low inflation reading was heavily influenced by a drop in energy costs, the steepest month-over-month decline in the price of used cars and trucks in 15 years and a strong dollar that has held down the price of other commodities in recent months.

Rising interest rates and faster economic growth in the U.S. compared with other developed economies have helped push the dollar higher in recent months, which is likely keeping a lid on the prices of goods either purchased overseas or that compete with imports. The WSJ Dollar Index, which measures the greenback against a basket of other currencies, rose about 7% from April to September.

Energy prices, which have risen nearly 5% over the past year, slipped 0.5% in September, as gasoline prices fell 0.2%.

Economists said that although lower gasoline prices dragged down inflation in September, that’s unlikely to repeat in October since prices at the pump have risen in the early part of this month.

The decline in used auto prices is also likely to reverse in October as Americans hit by Hurricanes Florence and Michael replace damaged vehicles.

In a positive sign for American workers, modest prices increases caused the pace of inflation-adjusted earnings to rise at the strongest rate in six months, according to Thursday’s report. Average hourly earnings rose a seasonally adjusted 0.3% in September.

With unemployment down to 3.7%, wages may finally be picking up. Hourly wages, adjusted for inflation, were up 0.5% in September from a year earlier, and though that isn’t spectacular, it’s the strongest year-over-year pace since January.

With the jobless rate in September at the lowest level since the Vietnam War, some companies are raising wages to attract and retain workers.

Costco Wholesale Corp. boosted entry-level hourly pay by $1 to $14 earlier this year “and I believe that you’ll see more pressure on it,” Chief Financial Officer Richard Galanti said last week after the retailer posted strong sales growth in its most recent quarter.

Some retailers are also raising prices this quarter to combat wage inflation. PepsiCo Inc. Chief Financial Officer Hugh Johnstonsaid last week that rising transport costs due to a shortage of truck drivers mean it will increase prices on single-serve Frito-Lay products by 4% to 5% in the fourth quarter.

Fed Chairman Jerome Powell wants to raise rates gradually over the coming year, premised on the assumption that core inflation is gradually rising.

The Fed has “got time to assess this and other reports” before the central bank’s Dec. 18-19 policy meeting, said JPMorgan Chase & Co. economist Michael Feroli, when officials will next submit projections for the economy and interest rates in years to come. Thursday’s CPI report is “one piece in a bigger puzzle,” he said.

Fed policy makers in September raised their benchmark short-term interest rate to a range between 2% and 2.25%. Officials signaled they expected to lift the rate again later this year and through 2019 to keep a strong economy on an even keel.

The risk that inflation climbs higher and faster than anticipated could require the Fed to raise rates “a little bit quicker,” Fed Chairman Jerome Powell said at his Sept. 26 press conference. He added, “We don’t see that. We really don’t see that.”

“Inflation is low and stable,” he said.

—Theo Francis contributed to this article.

Write to Harriet Torry at harriet.torry@wsj.com