The incident happened at a nightclub. according to a statement by the ECB, and is being investigated with both players now set to miss the second Test, starting at The Oval on 17 June.
The statement from the ECB said: "The ECB is currently investigating a breach of team protocols following the conclusion of the first Men's Test against New Zealand.
"Ben Stokes and Gus Atkinson were present at a nightclub in the early hours of Monday morning when an incident took place. We are currently seeking further information, and an announcement regarding the squad for the second Test will be made in due course.
"The Cricket Regulator has been informed and we will provide a further update when possible."
The current England team have been criticised for their off-the-field behaviour in the last year, with vice-captain Harry Brook fined and reprimanded after a late-night incident involving a bouncer in New Zealand.
Ben Duckett was filmed being drunk on a night out during a controversial mid-series break when playing against Australia with the team culture coming under intense scrutiny.
Rob Key, England's managing director, denied that the team had a "drinking problem" in the aftermath of the Ashes but conceded: "There's two or three players that can be irresponsible with alcohol given that opportunity."
Jordan Cox and Sonny Baker are set to make their Test debuts for England against New Zealand after the hosts announced their XI ahead of the second game of the series, starting at the Oval on Wednesday.
England have added seamer Henry Crocombe to their squad ahead of the second Test against New Zealand after Ollie Robinson experienced knee soreness in training and is set to have a scan.
Former England captain Michael Vaughan believes it's an overreaction to remove Ben Stokes as Test captain for breaking curfew.
Joe Root will stand in as England captain for the second Test against New Zealand after Ben Stokes and Gus Atkinson were made unavailable following a breach of team protocols.
