In a segment to recognise past winners, a Zoom-style call was organised with some of the recipients of the award.
Sir Jackie, who won the BBC accolade in 1973, could be seen lying in a bed in hospital.
Viewers took to Twitter to express their concern.
In a video message to this year’s SPOTY winner Lewis Hamilton, Sir Jackie revealed he was suffering from a “knee problem”.
Posting on Instagram, the 81-year-old Scot said: “Lewis, many congratulations for winning one of the best things to win, the Sports Personality of the Year award. I was lucky enough to win it as well and it must be very satisfying for you.
“Sorry, I’m in hospital at the present time as I have a knee problem. You’ve had a hell of a season - all the very best.”
He added on his account: “You’ve been a champion on the track in racing, and a champion for voices around the world off the track.”
Hamilton replied: “Thank you Sir Jackie. Get well soon.”
The 35-year-old capped a memorable year on a personal level by winning the public vote for the prestigious BBC prize, after securing a record-equalling seventh Formula One title.
However, in a year notable for sports stars becoming effective campaigners in a wide range of areas, Hamilton’s advocacy for the Black Lives Matter movement was just as important to him as his exploits on the track.
Hamilton, who finished ahead of Liverpool and England footballer Jordan Henderson and jockey Hollie Doyle, told BBC Breakfast after his victory: “I feel like I’ve really found my compass this year.
“I feel like there’s this huge amount of work to do in so many areas. And this is really probably one of the first years I felt like I’ve had something different driving me at the core, pushing for diversity within our industry, using my voice for something far bigger than myself.”
Sir Jackie won the Formula One world title three times, in 1969, 1971, 1973. He was also a strident campaigner for making the sport safer.