Pesticide companies and farmers could soon face a raft of costly delays related to the monthlong government shutdown.

With the Environmental Protection Agency closed, including its Office of Pesticide Programs, the process for approving new pesticides has ground to a halt.

“Pesticides are among the most heavily regulated products in the country,” said Chris Novak, president of CropLife America, a trade organization representing agricultural pesticide companies.

“Our members and their farm customers depend on predictable regulatory and scientific...