NASCAR suspended Allmendinger until further notice last week after two samples he provided tested positive. The racing organization gave the 30-year-old driver a letter outlining what he needs to do to gain reinstatement.
NASCAR doesn't disclose what type of drugs its testing program finds, but Allmendinger's business manager, Tara Ragan, said the driver tested positive for an amphetamine.
"I apologize for the distraction, embarrassment, and difficulties that my current suspension from NASCAR has provided," Allmendinger said in a statement.
He said he is in NASCAR's "Road to Recovery" program and wants to return to NASCAR racing "in the near future."
Sam Hornish Jr. will drive Allmendinger's No. 22 car for the time being.
Penske team owner Roger Penske said he was "disappointed with A.J.'s positive drug test results."
"A.J. is a terrific driver, a good person and it is very unfortunate that we have to separate at this time," he said.
"As A.J. begins NASCAR's 'Road to Recovery' program, we wish him the best and look forward to seeing him compete again in NASCAR."
Allmendinger is the second Sprint Cup driver to be suspended since NASCAR revised its drug policy before the 2009 season. Jeremy Mayfield failed a drug test in May 2009 and has not competed in a NASCAR race since.