Rodriguez was arrested Tuesday after two women told police he molested them back in the 1990s when they were each 14 years old.
Rodriguez is being held on $200,000 bail.
The 66-year-old is part of the musical duo Cecilio & Kapono. The group formed on Oahu's North Shore in 1973 when Rodriguez and Henry Kapono were introduced by mutual friends, according to the group's website.
The group was on the mainland for a "Back in the Day Good Times Together" tour and performed a week ago in Redondo Beach, Calif.
Kapono, on a Disneyland vacation with his family, issued a statement Thursday reacting to the arrest, which he said he just recently learned about. "I did not see this coming," he said. "I am saddened for Cecilio and heartbroken for the family involved. My heart and prayers go out to them."
In 1994, Rodriguez pleaded no contest to attempted sexual assault in a Hawaii court. In August, he was found guilty of driving under the influence of an intoxicant on Oahu.
The Associated Press contributed to this report.