Stokes and bowler Gus Atkinson are facing a probe by the England and Wales Cricket Board (ECB) for breaking team curfew rules on Monday morning following England's win in the first Test against New Zealand at Lord's.
The pair were also reported to have become involved in what became a physical confrontation with the rugby player.
A security guard who was with the England duo was reportedly injured in the incident.
It is the latest controversy concerning the England team following a tour of Australia where the side faced allegations of a drinking culture during a 4-1 Ashes series loss concluded in January.
The squad announcement for next week's second Test at the Oval has been delayed and there are now growing concerns over whether Stokes can continue as England captain.
"He's in severe doubt," Gower told the BBC on Tuesday.
"One of the responsibilities as a captain is to set the right tone; if you're leading, you have to set the right example."
The 69-year-old, one of the outstanding batsmen of his generation, added: "They have to sort it out. If you've agreed to a curfew you have to abide by it.
"I've got a lot of respect for Ben and most the things he's done for the last three years or so as England captain.
'Bad position'
"He has become - or, I probably have to use the past tense now - had become, a very important figure as a leader of that team. I don't know what he's thinking at the moment... regret could be the least of it. He will be mortified, I'm sure, to have put himself in that position in the early hours.
"It's a misjudgement. You've put yourself in a bad position and you've put yourself at risk."
Stokes, 35, spoke of giving up alcohol during his recovery from injury last year but soon after England had wrapped up a dominant 115-run against New Zealand at Lord's to go 1-0 up in a three-match series, he told reporters: "I won't be really happy until I get to share a beer with the boys."
If Stokes is stripped of the captaincy, vice-captain Harry Brook - already the skipper of England's white-ball teams - could lead the hosts at the Oval.
This would represent a remarkable reversal of fortune for Brook, who was fined and censured for late-night drinking and clashing with a nightclub bouncer before captaining England in a one-day international in Wellington in October.
That episode led England to impose a midnight curfew on all players and staff.
In 2017, Stokes was involved in an incident outside a nightclub in Bristol, southwest England, that led to him being charged with affray.
He subsequently missed the Ashes tour of 2017/18 before he was found not guilty of the charge following a trial at Bristol Crown Court in August 2018.