The shooting came 24 hours after 18-year-old Luke Wilson was shot in the head and neck in Inchicore's Memorial Park.
It is understood that after being shot, Mr Rice managed to make his way to his girlfriend's house where she raised the alarm. No arrests have been made so far over the incident.
Mr Rice was rushed to Connolly Hospital in Blanchards-town where he was still being treated today.
Meanwhile, detectives investigating the shooting of Luke Wilson are still quizzing the 19-year-old man arrested on Sunday evening. Luke is understood to be making a good recovery after his miracle escape after he was shot twice in the head.
Sources say that the arrested man -- who is well known to Luke Wilson and also from Ballyfermot -- is the chief suspect.
The Herald revealed yesterday that Luke was targeted because of a brutal pub fist fight the previous weekend.
Sources say that the row between Luke and the other man may have kicked off over "a minor debt", but turned more violent when the other man started abusing the memory of Luke's uncle John.
The man involved in the pub row with Luke is not suspected of involvement in Sunday's shooting, which happened at 3pm, but one of his best friends is the teenager in custody.
Gardai have yet to find the gun. Searches of the park continued yesterday while properties in the Ballyfermot area were also raided by gardai.
Sections of the Memorial Park in Inchicore are a popular haunt for criminals as it is an easy place to hide weapons and drugs, according to sources.
"There is a lot of dense undergrowth -- lads are always stashing stuff there," said a source.
Luke's mother Debbie Wilson died in February 2008, after years of heroin abuse.
Luke's uncle John (35) was shot dead last September, his uncle Eric is serving a 23-year sentence in Spain for murder, while another uncle Keith (25) is serving a life sentence for a 2010 Finglas gangland murder.