The England and Wales Cricket Board's (ECB) investigation into the actions of Stokes and Atkinson is still ongoing.
An ECB statement said: "Given the ongoing investigation, Ben Stokes and Gus Atkinson have not been made available for selection for the second Test against New Zealand."
The Cricket Regulator is conducting a separate investigation, one that might not be concluded for a number of weeks.
Stokes, 35, has been given time by the ECB in order to consider his options. The governing body has denied any suggestion he has been asked to resign.
The episode is an unwanted controversy for the ECB following a dismal 4-1 Ashes tour of Australia that was dogged by off-field controversy.
The defeat of New Zealand in the first Test at Lord's looked to be a small step in the right direction, but now England will have to attempt to win the series without their captain and all-rounder, and a key pace bowler.
Though Stokes' poor batting form has come under scrutiny, his all-round abilities are vital to balance the XI.
Atkinson, 28, endured a poor winter, yet looked back to somewhere near his best with seven wickets in the first Test.
The Surrey man has now surrendered his place in the England team on his home ground and his absence could mean a return for Archer, who missed the first Test following his stint at the Indian Premier League.
Depending on conditions, the best replacement for Stokes would be spin-bowling all-rounder Rehan Ahmed, who is retained in the squad after missing out on the final XI at Lord's.
It would be tough on Shoaib Bashir – the off-spinner was in the XI at Lord's and was not required to bowl a ball. If Ahmed replaces Stokes, Bashir would then make way for England to field four specialist seamers.
If England decide to replace Stokes with a specialist batter, uncapped James Rew was in the squad for the first Test.
Essex's Cox, 25, has been in a number of England Test squads but is yet to make an appearance. He was due to make his debut as wicketkeeper on the tour of New Zealand in 2024, only to suffer a broken thumb in the nets.
Root's return to the captaincy is an indictment of the situation the ECB found themselves in.
It would have been difficult to have one captain, Stokes, unavailable for a nightclub incident, only to replace him with Brook, eight months on from his own nightclub misdemeanour.
Therefore Root will lead England at least once more, and perhaps even for the third Test at Trent Bridge a week later.
Root's elevation could be a hint towards an expectation that Stokes will eventually return to the job.
If Brook had been made captain, there would have been the opportunity to demonstrate the Test team in his image, especially with Stokes' playing powers appearing to be on the wane.
Instead, with Root named as interim captain, there looks to be a path for Stokes to return if he desires.
If the all-rounder misses the remaining Tests against New Zealand, his comeback could be for the three-Test series against Pakistan in August.
Earlier on Wednesday, ex-England skipper Michael Vaughan said Stokes should not lose his job as captain.
"Yes, Ben Stokes broke a curfew. Yes, he made a mistake. But is that a sacking offence as England's Test captain? I don't think so," Vaughan wrote in the Telegraph.
"The ECB has to be brave enough and strong enough to do what it thinks is right. If that is to sack him then fine, but I do not agree with that decision on this issue."

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