The 72-year-old Briton travelled to Park City, Utah to see actress turned director Annabelle Dexter-Jones's first film - a short titled Cecile on the Phone.
However the I Want To Know What Love Is rocker had to leave the event early, after falling ill due to the lack of oxygen in the air in Park City, which is more than 2,000 metres above sea level.
"Mick had a bit of altitude sickness and decided to leave prior to Annabelle's event," a representative for the rocker told the New York Post's Page Six gossip column. "He is now back in NYC (New York City) and in good health and spirits."
Anabelle's mother, Ann, and her brother, Alexander, attended the prestigious movie event.
Cecile on the Phone follows a New York woman as she agonises over her relationship with her ex-boyfriend in a number of phone conversations.
Sundance has been the venue for a number of major short film premieres this year (17), with Kristen Stewart and her on-off lover St. Vincent both screening their first directorial efforts.
Among the feature films generating critical buzz at the festival is 2017 Oscar nominee Casey Affleck's latest directorial endeavour, A Ghost Story.