The England and Wales Cricket Board are investigating Ben Stokes and Gus Atkinson over an incident at a nightclub.
An ECB statement announced that the pair "breached team protocols" early Monday morning.
The ECB said in a statement: "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 investigation is understood to concern more than simply breaking the curfew that remains in force for all England players and staff.
It is the latest controversy to hit the England team, just after their win at Lord's on Sunday.
Ben Stokes is under investigation by the ECB
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A midnight deadline was introduced following an incident in Wellington before the Ashes, when white-ball captain Harry Brook was struck by a nightclub bouncer on the eve of a one-day international against New Zealand.
That restriction was initially implemented for the Sri Lanka white-ball tour in January and the subsequent T20 World Cup, continuing into the current Test summer under Stokes' captaincy.
England were criticised for their off-field behaviour during their heavy defeat to Australia.
Atkinson was involved in an incident with Stokes outside a nightclub
| PADirector of cricket Rob Key conducted an investigation into the Noosa excursion but rejected suggestions that the squad had developed a drinking culture.
The Brook incident in Wellington only came to light at the conclusion of the Ashes series in January, with the batsman initially claiming he had been alone at the nightclub before it emerged that Jacob Bethell and Josh Tongue were also present.
Speaking after Sunday's victory at Lord's, Stokes had expressed his eagerness to celebrate with teammates.
Stokes had expressed his eagerness to celebrate with teammates after Sunday's win
| GETTYHe said: "I'm not going to lie, I'm very, very happy that we've won this week.
"I knew how big this game was in terms of the result and how it was going to be perceived externally if it didn't go well.
"I won't be really happy until I get to share a beer with the boys."
England's squad announcement for the second Test at The Oval, starting June 17, could now be affected by the investigation's outcome, with both Stokes and Atkinson potentially being left out.
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