TV star Garraway opened up about the taxi incident on the ITV show during a discussion about ambulance waiting times and whether the NHS could send taxis out on calls to relieve some of the pressure on the health service.
The broadcaster was talking about how ambulances can be delayed but said if you tried to book an official car "you can sometimes be waiting five hours for them to bring you home from hospital".
Explaining what happened with Draper, she said: "He was in a lot of pain, it wasn't sustainable.
"So we took a cab home from the hospital and we went over a speed bump and he slipped out of the wheelchair."
"Something you never envisaged happening?" said her co-presenter Ben Shephard.
Garraway, 55, went on: "Well it's hard isn't it?
"It's hard to deal with."
"You want someone with you to manage that," she went on.
"And I was really lucky because the cab driver, black cab driver, that had a mobility access, his father he had cared for post a stroke.
"So he was really good at handling someone with that condition.
"So the two of us were hauling him back into the wheelchair, strapping him in and got him home."
Draper first fell ill in March 2020.
He returned home to Garraway and their two children - Darcey and 13-year-old son Billy - in April 2021.
Watch: Kate Garraway gives update on husband's long wait for Covid care