Wolstenholme has been sober since the release of their LP The Resistance in 2009.
Drummer Dom Howard has revealed that his bandmate was given an ultimatum by himself and Matt Bellamy over his dependency on alcohol.
Howard stated that they told Wolsenholme that his habit was starting to have a negative influence on the band's future.
"For some reason he could still play the bass, even though he was s**tfaced," Howard told The Observer.
"He was drinking on stage. I started counting how many drinks he was having during the set and I could see him getting more and more glazed. By the point we came off stage, he'd be f**ked. It just got too weird."
When asked whether the band told him to seek help, he said: "Yeah, a few times. Chris now says things like, 'I can't believe they put up with me for ten years'. Which is true. I can't believe we did. But we did. I've always believed in band integrity and sticking together."
Wolstenholme revealed last year that he quit drinking after he began vomiting blood following a heavy session.
Muse release their new album The 2nd Law tomorrow (October 1).
Watch the music video for Muse's new single 'Madness' below: