The Serbian joined the Red Devils in July in a £40m ($52m) move that saw him become Jose Mourinho's third signing of the summer following the arrival of Victor Lindelof and Romelu Lukaku.
In a deal questioned by many, Blues boss Antonio Conte recently expressed unhappiness over the transfer, citing Matic's departure as a "great loss".
This led Gary Neville to speculate that Chelsea did not voluntarily sell Matic and Lampard believes the possibility of that is likely as he too was surprised that the Premier League champions would sell a key player to a direct rival.
"I was surprised because selling to a direct rival isn't the norm at the top end," Lampard told ESPN FC.
"It was a big deal when Chelsea sold Petr Cech to Arsenal. People at the club seemed to mull it over for quite a while and then out of respect for Petr and what he'd done, and the situation with [Thibaut] Courtois, they let him go."
"This doesn't seem quite the same, but at the same time we don't know whether Matic wanted to leave. Was it his dream to go and play for Manchester United? Did he want a new challenge at 29?
"There are a lot of variables that aren't easy but from the outside, it does seem strange to let that player go to a direct rival — and he will improve them.
"It was certainly a position that Manchester United as a team needed to strengthen, and they've gone and done it with Matic."
Matic had a solid debut for the Europa League champions despite a 2-1 loss against Real Madrid in the European Super Cup earlier this week and will make his official league debut against West Ham United on Sunday (13 August).