A spokesman for the senator said Kennedy's wife, Vicki, would be in his place at the at St. Francis Xavier Roman Catholic Church in Hyannis.
Among the invited guests are Vice President Joe Biden, Oprah Winfrey, Jon Bon Jovi, Stevie Wonder and Massachusetts Gov. Deval Patrick.
Hundreds of people gathered outside the church before the service for Shriver, the founder of the Special Olympics who died Tuesday at age 88.
A mother and son who were both Special Olympians led the funeral procession carrying the Special Olympics torch.