Sonny Kiernan, 12, was found dead in bed at his father’s property in Glasgow’s west end on Monday night.
He was taken by ambulance to the nearby Royal Hospital for Sick Children at Yorkhill but could not be saved.
Police said they were investigating the “unexplained death” and a post mortem would be carried out.
But there are not thought to be any suspicious circumstances.
Sonny Kiernan, a Kelvinside Academy pupil, lived at the townhouse flat with his 51-year-old comedian father, his mother Lesley, 44, and 14-year-old sister, Kaye.
Comedian and TV entertainer Andy Cameron tweeted: “Dreadful news about young Sonny Kiernan.
“My thoughts are with Ford and his family. Sometimes this life is impossible to understand. RIP Sonny.”
Sonny Kiernan’s death comes as Ford Kiernan and his Still Game co-star Greg Hemphill are due to revive their hit show on stage.
Before that Ford Kiernan and Greg Hemphill enjoyed massive success with Chewin’ The Fat.
In 2001, Ford Kiernan and Greg Hemphill had celebrated becoming fathers by giving their sons starring roles in their show in 2001.
A three-month-old Sonny Kiernan and Benny Hemphill – born just 10 days apart – made their screen debut in the fourth series of the hit comedy.
At the time, Ford Kiernan joked: “We’ve negotiated separate pay cheques for them, but we stopped short of their demands for their own <<Sonny and Benny>> sketch.
“We’re all very close so they’ll grow up great pals, but I doubt they’ll end up a double act like their dads.”
However, Ford Kiernan and his wife had shielded their children from the limelight.
Sonny Kiernan’s teachers at Kelvinside Academy also paid tribute to the youngster.
A spokesman for the school said staff were “devastated” to hear of the death of the “lively, outgoing pupil”.
“Our thoughts, prayers and deepest sympathies go to Mr. and Mrs. Kiernan and Kaye for their tragic loss,” he added.
“Sonny was a lively, outgoing pupil with a warm smile and a great sense of humor.
“He made a whole-hearted contribution to the school community, bringing infectious enthusiasm to lessons and activities.
“We shall always remember him as a cheerful boy who brightened our lives.”
A Police Scotland spokeswoman said: “Around 11.30 p.m. on Monday January 6, police received a report of the death of a 12-year-old boy in Glasgow.
“A post-mortem will be carried out in due course to establish the exact cause of death.
“The death is currently being treated as unexplained and inquiries are continuing.”
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