The Daily Telegraph said the 28-year-old defender was ordered to train with the club's development squad after manager Terry Connor was made aware that he was under the influence of alcohol.
Johnson, who was fined two weeks wages following the incident, issued a short statement apologising for his behaviour.
"My conduct and approach to training on Monday was below the high standard the club rightly needs and demands of me, and what I demand of myself," he said.
"As a result, I have apologised to the manager, my team-mates and the club."
The incident occurred on Monday, with several of Johnson's team-mates remonstrating with him over his condition.
Interim manager Connor said Thursday he had no plans to strip Johnson of the club captaincy.
"Roger reported for work and he wasn't fit to train - or fit to train properly," Connor said. "He made a mistake on Sunday night, he came in on Monday morning, we dealt with it on Tuesday.
"I spoke to him and said 'what you did was unacceptable'. We dealt with that matter, we finished with it on the Tuesday and we have moved on from there.
"I would be disappointed with any player who came in not fit to train properly. He has apologised for it, he came in, he knows he did wrong, and he has taken his punishment."
Asked if Johnson could be replaced as captain, Connor replied: "I've got no immediate plans to change anything. It has been dealt with."
Johnson joined Wolves from Birmingham last summer but has been unable to prevent a poor campaign which has left the club languishing third from bottom.
Source: AFP
Source: AFP