The 30-year-old Sprint Cup Series driver failed the initial drug test of his "A" sample taken the last weekend in June while he was competing at Kentucky Speedway. Allmendinger said in a statement he is petitioning NASCAR to test his "B" sample.
NASCAR officials said prior to a race at Daytona International Speedway Saturday that Allmendinger was suspended "based upon notification of a positive 'A' test the racing organization received from the medical review officer.
Tuesday was the deadline for Allmendinger to appeal.
"I have informed NASCAR that I have requested that the 'B' sample be tested, following the steps according to NASCAR's 2012 rule book regarding this situation," Allmendinger said in his statement. "I fully respect NASCAR's drug usage policy and the reasons they have it. I am hoping this can get resolved as quickly as possible so that I can get back to driving the No. 22 Penske Racing Dodge."
NASCAR has not revealed the substance detected in the driver's sample.
Allmendinger is in his first year as driver of the No. 22 Dodge for Penske Racing. He replaced Kurt Busch, who was dismissed from the team following the 2012 Sprint Cup season.
Sam Hornish Jr. is subbing for Allmendinger during his suspension.