"We have a surprise that's not on the programme, but we are incredibly grateful and honoured to have a singer who my grandmother loved," Ethel Kennedy's grandson Joe Kennedy III told the funeral attendees.
President Biden, who spoke at the end of the service, became visibly emotional while listening to the song.
Before Sting performed, country star Kenny Chesney spoke about his friendship with Ethel and her daughter Rory Kennedy, and sang You are My Sunshine.
Joe Kennedy later told the audience he was "honoured to announce one final surprise" before Biden's eulogy, introducing Stevie Wonder as a "dear friend of my grandfather and grandmother".
He sang The Lord's Prayer before going into a special rendition of Isn't She Lovely. He inserted Ethel's name into the song and called for the audience to sing along while he played the harmonica.
Ethel Kennedy, who was the widow of former Sen. Robert F Kennedy, died at 96 years old last Thursday. Robert F Kennedy was assassinated in June 1968 while he was running for the Democratic presidential nomination.
