Videos circulating on social media on Sunday appeared to show Carse in handcuffs, being led away from a club by four police officers.
The Durham bowler, who is England's squad for the second Test against Pakistan this week, was seen with team-mate Matthew Potts.
"We are aware of an incident which is reported to have taken place in Derby last night, and are currently investigating," an ECB statement read.
"We will provide a further update when possible."
