Allmendinger, 27, who drives for Richard Petty Motorsports, was pulled over in the early hours of Thursday morning and failed a sobriety test according to the Associated Press.
It is unclear how the issue will affect Allmendinger, who remains, for the moment, listed as the driver of the number 44 car for this weekend's race at Talladega.
He is expected to take over the iconic number 43 car for next year, when RPM merges with Yates Racing and becomes a Ford.
Richard Petty's squad has traditionally refused to be involved with any kind of marketing or sponsorship activities involving alcohol.
This year however, one of his cars is sponsored by Budweiser in a deal carried over through the team's purchase of Gillett Evernham Motorsports.
Sadler gets a Ford for TalladegaInterest mounts in Canales
