Carse was arrested on suspicion of being drunk and disorderly in Derby city centre on Saturday night before being released after agreeing to leave the area. Social media footage appeared to show the 31-year-old being led away from a nightclub in handcuffs by police.
The England and Wales Cricket Board (ECB) confirmed on Monday that Carse would miss Thursday's Test at Lord's while the investigation continues. Hampshire seamer Sonny Baker has replaced him.
"Brydon Carse will no longer be available for selection for the second men's Rothesay Test match while this investigation is ongoing and the full facts are obtained," the ECB said.
Carse had been playing for Durham after missing England's XI for the first Test at Headingley. He and Matthew Potts featured in Durham's 338-run County Championship victory over Derbyshire on Saturday.
Potts and former England captain Ben Stokes were also seen in footage from the incident, although there is no suggestion either committed an offence.
The incident comes just days after Test captain Joe Root confirmed England had scrapped their midnight curfew. The policy was introduced following several off-field incidents on tours of New Zealand and Australia, including white-ball captain Harry Brook's altercation with a nightclub bouncer in Wellington.
Stokes and Gus Atkinson were also suspended following celebrations after England's first Test against New Zealand. They were cleared of violent conduct but received written warnings for breaching contractual obligations.
Joe Root has admitted he is "really hacked off" by Brydon Carse's latest off-field controversy, insisting England must rebuild trust after the fast bowler was withdrawn from the squad for the second Test against Pakistan.
Dhruv Jurel struck the second Test century of his career as India strengthened their grip on the second Test against Sri Lanka.
Pat Cummins has welcomed Australia's long-awaited return to South Africa, describing the Proteas as a "really strong side" as the visitors begin preparations for a three-Test series in October.
Devdutt Padikkal continued his outstanding start to the Test series with a second successive century as India reached 300-5 at stumps on day one of the second Test against Sri Lanka in Colombo.
