New York moved to become the first city in the U.S. to cap ride-hailing services including Uber Technologies Inc. and Lyft Inc., freezing new vehicle licenses for one year while it studies the fallout from the booming industry.

The vote Wednesday by the New York City Council could cripple the growth of Uber and Lyft in their biggest U.S. market as both companies are heading toward eventual initial public offerings. The Silicon Valley companies’ businesses depend on recruiting as many drivers as they can to drive down fares...