Allmendinger was suspended shortly before Saturday night's race at Daytona for failing a random drug test. NASCAR and Penske officials have not said what Allmendinger tested positive for, and Allmendinger has made no statement since his suspension.
Allmendinger has until Tuesday to ask for his "B'' sample to be tested.
Penske Racing says in a Monday statement that it will continue to work with NASCAR on this matter, but the team will use Hornish in the No. 22 Dodge this weekend.
Hornish was the emergency substitute for Allmendinger on Saturday night. He flew to Daytona from Charlotte and arrived right before the start of the race.