The Blues have made some high profile transfer gaffes in the past, with the London side having failed to give the likes of Romelu Lukaku and Kevin De Bruyne adequate time to shine before selling them on and having to watch them become Premier League stars.
But Wilkins, who had stints as assistant manager – and caretaker – on two separate occasions at Stamford Bridge, believes the sale of Matic trumps the lot.
“It's the worst decision I've ever seen,” Wilkins told Sky Sports.
“You've got a guy here who was paramount to Chelsea along with Kante in the middle of of the pitch, winning the title with Chelsea the year before and all of a sudden you've sold him to one of - or the biggest - rivals we have.
“I say we because I am a Chelsea supporter so I'm speaking from the heart when I speak. I just could not see that for the life of me. Why would we let Nemanja go there?
“He's been outstanding for us and you've seen in the short period that he's been there [at Man Utd] how he's allowed Pogba to basically do what he wants.
“I just couldn't see that piece of business at all.”
Matic scored four goals in 121 appearances for Chelsea, winning two Premier League titles, a League Cup and the FA Cup.
The Serbia international has played every minute in the league this season for Jose Mourinho's Red Devils, who sit top of the table after three games with three wins.