Shane O’Connor, 17, was found dead after vanishing from Tallaght Hospital in Dublin on Thursday.
He was laid to rest after a ceremony with 50 mourners at Newlands Cross Cemetery and Crematorium in West Dublin.
The singer shared her grief on social media.
She wrote on Twitter: “We just said goodbye to our beautiful angel, Shaney.
“Very lovely Hindu ceremony. Shane will have loved it. He was always chanting “Om. Shanti”.
“I put a few packs of fags in the coffin for him in case there’s none in heaven.
“He’ll have loved that too. Om. Shanti.”
The grieving mother confirmed earlier this week that the teenager had died and described him as the “light of my life”.
The Nothing Compares 2 U singer earlier told of her pain after identifying his body, saying: “I have now formally identified the remains of my son, Shane.
“I’m going to take private time now to grieve my son.”
The mother of four confirmed her son’s death on social media.
She wrote: “My beautiful son, Nevi’im Nesta Ali Shane O’Connor, the very light of my life, decided to end his earthly struggle today and is now with God.
“May he rest in peace and may no one follow his example. My baby. I love you so much. Please be at peace:”
She later tweeted a Bob Marley song which she dedicated to Shane: “This is for my Shaney. The light of my life. The lamp of my soul. My blue-eye baby.
“You will always be my light. We will always be together. No boundary can separate us.”
Police had previously issued an appeal for the missing teenager.
He was seen in the CCTV image wearing dark jeans, a black hoodie with a colourful symbol on the front, a dark red top and white trainers.
A spokesman for the Gardai said: “Following the recovery of a body in the Bray area of Wicklow on Friday, 7th January 2022, a Missing Person Appeal in respect of Shane O’Connor, 17 years, has been stood down.”
A spokesperson for Sinead O’Connor said: “Regrettably, we can confirm the passing of Shane O’Connor.
“We politely ask for respect and appreciation for Sinead, Shane’s father and Shane’s family at this most difficult time.”