Recent changes in the handling of petitions for temporary visas for skilled foreign workers are raising concerns about the future of the program and what it means for certain industries.

Starting April 3, U.S. Citizenship and Immigration Services won’t allow “premium processing” for H-1B visas. That process allows employers to pay extra to get a decision in 15 days. The suspension of premium processing will last for up to six months so that the agency can reduce processing times for...