Around 200 people, largely members of her family and close friends, gathered at Saint Ailbe's church near Limerick.
Her mother, three children, six siblings and the other three members of the Cranberries were among the congregation.
The ceremony, broadcast live online by a radio station, began with a recording of her 1995 duet of Ave Maria with the Italian opera giant Pavarotti.
At the end of the service, her coffin was carried out to the sound of the Cranberries' song When You're Gone.
She was buried in a local cemetery in a private ceremony attended only by family members.
London coroner Stephen Earl said last week that he was awaiting test results following a post-mortem, with a full inquest set for April 3.
O'Riordan's death is not being treated as suspicious.