SAN FRANCISCO—A former engineer’s published allegations that she was sexually harassed at Uber Technologies Inc. during her tenure at the ride-sharing company created ongoing tumult that is unlikely to be settled solely by an internal investigation launched in its aftermath, labor and employment lawyers and experts say.

“The way this is being handled now could create a significant chilling effect and preclude perhaps many other female sexual harassment victims from coming forward,” said Kelly Armstrong, founding partner of The Armstrong Law Firm, a plaintiffs firm in San Francisco. Armstrong said she has been contacted by several female engineers at Uber since the controversy broke earlier this week.