Keith Brown, 55, entered his guilty plea to three felony counts.
Court records show Utah County prosecutors charged Brown with one first-degree felony count of sodomy on a child and two second-degree felony counts of sexual abuse of a child.
Brown could face a sentence of up to life in prison on the first-degree felony and up to 15 years each on the second-degree felonies.
Keith Brown appeared in court just three days after he and his wife were injured in a crash that saw his Porsche plunge from a mountain road into a 300-foot canyon in Utah.
Both parents survived the crash.
Brown's daughters are part of the classical piano group The 5 Browns whose albums have topped the classical music charts. The group has also appeared on "Oprah" and other shows.
The records in the abuse case don't identify any victim by name or indicate the relationship between Keith Brown and the alleged victims.
Court documents state the allegations stem from separate occasions between November 1990 and October 1992, November 1990 and November 1992 and March 1997 and March 1998 in Utah County.
Keith Brown was once the manager of The 5 Browns but now has no connection with them after the Brown children severed their professional relationship with him in October 2008.
The Associated Press contributed to this report.