The Scottish manager says the defender's switch is a "blatant manipulation of the rules" and has criticized Spurs chairman Daniel Levy
The 20-year-old looked set to join Spurs when his contract at Old Trafford expired on June 30 but the two clubs were unable to agree a compensation package.
Fryers instead moved to Liege on a two-year deal, meaning compensation did not have to be paid to United, and ended his spell in Belgium to sign for Tottenham on Thursday.
But Sir Alex believes the transfer has Spurs chairman Daniel Levy's fingerprints "all over it" and has called for the player's registration to be looked into.
"How would you put it? To me, I think it's a blatant manipulation of the rules," he told MUTV. "I think the league should look into it.
"I think the registration should be stopped until they investigate it thoroughly. There's bound to be a trail, either mobile phones or e-mails, that could give you the full story of it.
"I must say I'm disappointed in Tottenham. For whatever reason, a club that size has decided to go down this route. I'm disappointed."
Fryers initially joined up with Spurs on trial after his contract at United came to an end, even taking part in a pre-season training camp in Portugal.
Sir Alex added: "We knew immediately and suspected that he would return to Tottenham in January and that's happened. It's a Daniel Levy deal. You know, it's his fingerprints all over it. It's the kind of thing we expected he was going to do."