His wife, Barbara Robbin, who is understood to have found him dead, suggested that an epileptic fit could have been a possible cause for his demise.
Speaking outside the couple's home in Barnes, southwest London, she said: "We don't know yet what happened. He had a strong heart, so I don't think it was a heart attack. But we just don't know until the coroner's report."
The 58-year-old make-up artist went on to say: "Maybe he had a fit, maybe it was his heart. We just don't know."
A spokesman for the family said: "It is a terrible shock. All we know at this stage is that Rik died at home. We are all deeply saddened by this news, from the enormous number of fans Rik had to those who worked with him and knew him as a man as well as a fine actor. He touched many lives, and always for the better."
The couple, who married in 1985, have three children. Ambulance services and police were called to the house but Mayall was declared dead at the scene early yesterday.
Among those to pay tribute was Ade Edmondson, Mayall's writing partner and co-star in The Young Ones. They met at university almost 40 years ago.
Edmondson said they almost "died laughing" when they wrote together.
"They were some of the most carefree stupid days I ever had," he said. "And now he's died for real. Without me. Selfish b******."
One of the pioneers of the 1980s alternative comedy scene, Mayall found fame in The Young Ones, playing a deluded student radical.
He and Edmondson were also members of The Comic Strip Presents team alongside Dawn French, Jennifer Saunders (Edmondson's wife) and Alexei Sayle.
Other famous roles included Lord Flashheart in the Blackadder series and Alan B'Stard, the gloriously sleazy Tory MP in The New Statesman. His role as B'Stard ran from 1987-1993, winning a Bafta and an Emmy award.
Mayall also appeared in the Hollywood film Drop Dead Fred. He was cast as a poltergeist in the first Harry Potter film, only to find his scenes were edited out.
With typical humour, he laughed off the slight. "That was the best film I was in - and I wasn't in it," he said.
Mayall worked regularly last year, appearing in the Channel 4 sitcom Man Down and in the BBC's Jonathan Creek.
One of his last projects was a short animated comedy for Channel 4. Its title: Don't Fear Death.