9:54 AM PT -- NASCAR has issued a statement to TMZ Sports saying ... "We are aware of an incident that occurred last night and are in the process of gathering information."

"We take this as a serious matter and will issue a statement after we have all of the facts.”

Brian France -- the CEO and Chairman of NASCAR -- was arrested for DUI on Sunday evening in The Hamptons and cops say he was also in possession of oxycodone .. TMZ Sports has learned.

The 56-year-old -- one of the most powerful people in professional sports -- was initially stopped in Sag Harbor, NY while driving a 2017 Lexus. Cops say he blew through a stop sign at 7:30 PM.

During the stop, we're told officers suspected France was intoxicated and conducted a field sobriety test ... which France bombed.

We're told France's blood alcohol level was more than TWICE the legal limit. Cops say during the stop, they found oxycodone pills during a search of his person.

France was arrested and hauled to a nearby station where he was booked for DUI and criminal possession of a controlled substance in the 7th degree. France spent the night in jail and was released Monday morning after his arraignment.

And sources tell us ... during the process, France was name-dropping all of the powerful people he knew and even mentioned his relationship with President Donald Trump.

The France family is racing royalty -- Brian's grandfather Bill France Sr. (aka Big Bill) founded NASCAR back in 1948 and ran the organization. Brian's father took over the role from 1972 to 2000.

Brian has been CEO since 2003.

Sag Harbor is one of the most exclusive communities in the Hamptons -- where stars like Billy Joel have homes.

And, as one local puts it, "It's so stupid to drive drunk in the Hamptons. They have police checkpoints everywhere and police are always looking for drunk drivers."

Story developing ...