The funeral mass at St. Ailbe in Ballybricken, southwest Ireland, opened with a recording of "Ave Maria," sung by O'Riordan and Luciano Pavarotti.
Mourners included O'Riordan's bandmates, her ex-husband Don Burton and their three children, and the singer's mother and siblings. O'Riordan's boyfriend, Ole Koretsky, was also a member of the band D.A.R.K. with O'Riordan and Andy Rourke.
Items associated with the singer, including a guitar and a platinum disc, were laid at the altar.
Canon Liam McNamara said "no words are adequate to describe Dolores or to accurately state the influence for good she has been over the years."
"Now she is singing in the heavenly choir — hymns of petition for us," he said.
Kieran O'Reilly, the archbishop of Cashel and Emly, told mourners that O'Riordan's voice was "unique, far reaching and distinctly Irish."
"Her gifts have resonated in the lives of many and will continue to do so as her music and her songs will continue to be played and listened to," he said.
Funeralgoers broke out into applause when O'Riordan's coffin was carried out of the church to The Cranberries' "When You're Gone."
The Cranberries formed in Limerick, Ireland at the end of the 1980s and had international hits with songs including "Dream," ″Linger" and "Zombie."
O'Riordan's band mates paid tribute to the loss of their friend days after her passing.
"I am heartbroken and devastated by the news of the sudden and unexpected passing of Dolores. I have truly enjoyed the years we spent together and feel privileged to call her a close friend," Andy Rourke of The Smiths wrote on Twitter and Instagram. "It was a bonus to work with her and witness firsthand her breathtaking and unique talent, I will miss her terribly. I send my love and condolences to her family and loved ones. This photo was taken last NYE in NY with Dolores and Ole."
O'Riordan will be buried next to her father, Terence O'Riordan, at a cemetery in Friarstown.