Captain Stokes was left out of the ongoing second test along with bowler Gus Atkinson following an investigation into an incident in a London nightclub.
England's leading batsman Joe Root is interim captain at The Oval but Vaughan says the situation must be resolved quickly.
Asked to comment on reports that Stokes could return at Trent Bridge as a player rather than skipper, Vaughan told the BBC's Test Match Special: "If he resigns and stands down as captain, absolutely that can happen but if he's not resigning, then if he plays at Trent Bridge then England need Ben Stokes as captain. They need his leadership, his all-round ability, having an all rounder balances the side.
"I've read a few stories that he could return as a player only. Nonsense. If Ben Stokes plays at Trent Bridge then he has to be captain."
Stokes and pace bowler Atkinson broke the team's midnight curfew in the early hours of the Monday morning after the first test victory at Lord's and were reportedly present when a member of England's security staff was involved in an incident with a Saracens rugby player.
The Cricket Regulator - a separate body from the ECB - is also conducting an investigation, the ECB have said.
In the absence of Stokes, New Zealand are in a strong position after two days of the second test, with England trailing by 169 runs with four first-innings wickets left. The third test starts at Trent Bridge on June 25.
"I don't understand why we are in this situation still," Vaughan added. "I want to hear from the ECB publicly that Ben Stokes is the captain, he has done some good stuff for the England side. It's staggering. If they are sacking him then give us a reason why."
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