It is the latest controversy concerning the England team following a tour of Australia where the side was confronted with allegations of a drinking culture during a 4-1 Ashes series loss concluded in January.
"The ECB is currently investigating a breach of team protocols following the conclusion of the first Men's Test against New Zealand," the governing body said.
"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."
Before the Ashes, white-ball captain Harry Brook was punched by a nightclub bouncer in Wellington on the eve of a one-day international against New Zealand.
As a result, England imposed a midnight curfew on all players and staff.
The BBC, however, reported the curfew was still in place despite the first Test being over, and the investigation relates to more than a breach of the curfew.
England thrashed New Zealand by 115 runs before lunch on Sunday's fourth day at Lord's to go 1-0 up in a three-match series as they enjoyed a comprehensive victory in their first Test match since their humiliating Ashes defeat
The second Test, across London at the Oval, starts on June 17.