NASCAR made the announcement from its headquarters in Daytona Beach. Officials said Parrott would be suspended indefinitely.
Parrott, 49, is currently crew chief for the Richard Petty Motorsports' car driven by Aric Almirola. The Petty organization said Thursday Sammy Johns would take over Parrott's duties for this week race at the Talladega Superspeedway in Alabama.
Johns, vice president of operations and competition for the Petty team, said the organization is "very disappointed that one of our employees did not meet our expectations."
"We completely support NASCAR, their policies and final decisions when it comes to the substance abuse policy," Johns said.
Parrott was the crew chief for Dale Jarrett in 1999 when Jarrett won the series championship.
A report on NASCAR's web site said Parrott will be permitted to "return to competition upon successful completion of NASCAR's Road to Recovery treatment program."