Sonny Kiernan, 12, was found dead at the family's home in Glasgow's West End.
The father and son were known for joking together on Twitter, with the comic Ford affectionately calling his son "cheeky chops".
Sonny - the younger of the actor's two children - was found dead on Monday night in his bed.
As reported in later editions of last night's Evening Times, police said they were treating the death as unexplained and that a post-mortem examination would be carried out.
Showbiz friends of grief-stricken Ford rallied round him yesterday.
Scottish actor Greg McHugh said the youngster's death was "the worst news imaginable". He tweeted: "Shocked having just learned of Ford Kiernan's loss. Thoughts to his family."
Comic Andy Cameron, said: "Dreadful news about young Sonny Kiernan. My thoughts are with Ford and his family. Sometimes this life is impossible to understand."
Sonny, who was said to have a "great sense of humour", was a pupil at Kelvinside Academy, in the West End.
After learning of his death, the school paid an emotional tribute to the "lively, outgoing" pupil.
In a statement, school officials said: "We are devastated to learn of the death of Sonny Kiernan.
Sonny was a lively, outgoing pupil with a warm smile and a great sense of humour. 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."
Former First Minister Jack McConnell also expressed his condolences, describing Sonny's death as "devastating news".
When Sonny was born at the Queen Mother's Maternity Hospital in 2001, Ford was asked how the couple had chosen the name.
The comedian replied: "It was a nice warm day."
Ford, 51, lives in the Kelvinside house with his wife Lesley, 44, and their 14-year-old daughter Kaye.
The family moved in after selling their five-bedroom villa in Pollokshields in November.
The tragedy comes after Ford and his comedy partner Greg Hemphill reunited and announced plans for a Still Game comeback at Glasgow's Hydro arena. The run of live shows is due to start in the autumn.
Police confirmed they were called to the property at 11.30pm on Monday. A spokeswoman said: "Enquiries are continuing."