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.
They say officers saw indications France was intoxicated and found the pills during a subsequent search.
Details surrounding France's arrest were not released.
As law enforcement communicated with him, they became suspicious that he was intoxicated and had him undergo a field sobriety test, which he reportedly failed.
In a statement released Monday, NASCAR said: "We are aware of an incident that occurred last night and are in the process of gathering information".
TMZ first reported the story.
France publicly endorsed Trump for president in early 2016 at a rally in Georgia.
France was released just after 9 a.m. Monday. "We take this as a serious matter and will issue a statement after we have all of the facts". His grandfather, Bill France Jr., founded NASCAR in 1948.
NASCAR CEO Brian France was ran into trouble in the Hamptons on Sunday evening, according to TMZ Sports.
NASCAR CEO and Chairman Brian Z. France was arrested Sunday while allegedly driving under the influence and in possession of oxycodone.