The England and Wales Cricket Board (ECB) said in a statement it was investigating the incident, which involved Stokes and pace bowler Gus Atkinson.
"Ben Stokes and Gus Atkinson were present at a nightclub in the early hours of Monday morning when an incident took place." The ECB statement said.
"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 Lord's test, which England won by 115 runs, finished on Sunday (England time).
The statement said the pair were involved in a "breach of team protocols".
Last summer's Ashes tour was shrouded with allegations of a drinking culture within the England camp.
A video of batter Ben Duckett was posted on social media appearing to show him intoxicated while in Noosa.
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.
The latest breach adds renewed pressure on head coach Brendon McCullum, who retained his role across all formats in March following an ECB review, despite lingering concerns about team culture.
Stokes was previously involved in a 2017 incident outside a Bristol nightclub that led to an affray charge. He missed the 2017-18 Ashes tour before being cleared the following summer.
The second test will be at the Oval next week.
