Airlines can’t get permission to add new planes to their fleets. Mortgage lenders aren’t able to verify the income of borrowers. And brewers can’t sell new beers while label approvals are on hold.

In ways both small and large, businesses are beginning to feel the bite of the government funding impasse that has shuttered nine major departments, slowing federal reviews of everything from pipelines to mergers.

“The impact will multiply as the days and weeks continue,” said Stan Collender, a longtime congressional budget aide who now edits @thebudgetguy blog in Washington. “It’s only going to expand.”

The shutdown entered its...