Both could be dropped for the next Test after breaching team protocols after the Test win over New Zealand.
The revelation is a grievous blow to a team seeking to reset its image and relationship with fans after being dogged by allegations of a drinking culture and "lad's holiday" approach during the Ashes debacle.
Victory over the Kiwis at Lord's on Sunday, in the first Test since the 4-1 Ashes thrashing, was the first step to redemption, but it appears the celebration of that success could undo any positivity.
The England and Wales Cricket Board announced they were looking into a "breach of team protocols" as the pair were "in a nightclub in the early hours of Monday morning when an incident took place".
Stokes, 35, has been captain since April 2022 and formulated an enterprising approach to Test cricket alongside coach Brendon McCullum, which was dubbed "Bazball". After dramatic early success, results have nosedived and the team showed a more pragmatic approach at Lord's.
Atkinson, 28, took 5-30 in the second innings as England wrapped up a 115-run win over the Black Caps and is seen as a core part of England's attack.
The ECB added: "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 regulator is an independent disciplinary body that can impose suspensions and fines.
If Stokes is suspended then, with supreme irony, vice-captain Harry Brook would take over for the second Test at The Oval on June 17.
Brook was fined A$60,000 and given a final warning after an incident in Wellington on the eve of a white-ball match, in which he was captain, when he was hit by a nightclub bouncer.
Although the incident happened prior to the Ashes the news only broke after the final Test at Sydney. By then there had been numerous reports of excessive drinking on tour, in particular during a mid-Ashes break in Noosa.
While England director of cricket Rob Key denied the team had a drinking culture a midnight curfew was subsequently imposed for a white-ball tour of Sri Lanka and the T20 World Cup that followed, both with Brook as captain.
The curfew has remained in place and is believed to apply to evenings after a Test has finished.
Earlier this year McCullum said: "The day I walked into the job, the first thing I said to these boys is don't do anything that lands you on the front page of the paper, and nothing good happens after midnight, but we're going to have a good time."
