Cotterill, who had been at home with his wife, was hospitalised last Friday for extra oxygen and night time care as his condition worsened
But the Town boss improved over the weekend and is now 'on the mend', according to his assistant Aaron Wilbraham.
Shrewsbury's televised FA Cup third round tie at Premier League Southampton tomorrow will go on without the absent manager, who will be watching from his Bristol hospital bed.
Wilbraham and skipper Ollie Norburn said this morning that the manager's presence has been missed as the League One side attempt to prepare for an underdog clash without their leader.
"It's such a strange atmosphere without him, he's the energy around the place, everyone who knows him knows he's a ball of energy bouncing around. We've definitely missed him," said Wilbraham, who played under Cotterill at Bristol City.
"But he has been really poorly with it for the last two weeks. He was actually in intensive care over the weekend, he's had a really bad case of Covid.
"It got quite worrying at some points. We've all been wishing him well. I know him as a man and person and I know if anyone was going to take a bad case of Covid out of all of us he'd be the one stood at the front taking it for the team, players and staff. That sums him up as a person.
"It's been quite worrying. I've spoken with him in the last couple of days and I can tell he's getting better, his voice is getting better, he's starting to crack a couple of jokes, telling me to tell the boys he'll be watching from his hospital bed so they better be at it!
"So I know he's improving now, it's a bit of relief for everyone. It's been a crazy time.
"A lot of the players have been messaging because I've been keeping them in touch and it has lifted them (his recovery), everyone is really together as we have been since the gaffer took over.
"He is on the mend and improving, so it's definitely good signs after a worrying couple of weeks."
Town have been back in training at Sundorne Castle since Friday after 10 days off due to a widespread outbreak of Covid-19 that saw around 20 positive cases in the squad and staff.
One player is currently still isolating and will be missing for the Saints tie, while goalkeeper coach Brian Jensen and fitness coach Andy Johnson have not been able to return to training.