American shale drillers, which defied expectations and upended traditional oil markets by increasing production in the face of lower prices, are finally showing signs of slowing down.

The number of rigs currently drilling for oil in the U.S., typically viewed as a proxy for activity in the sector, grew 6% in the third quarter—a marked deceleration from the previous four quarters, when it rose more than 20% on average. Last month, the U.S. Energy Information Administration cut its forecast for U.S. oil production, saying it...