The 20-year-old has featured on six occasions in Premier League 2 this season, while he has also played twice in the EFL Trophy during the 2023-24 campaign.
Bennett is yet to make his first-team debut for the 20-time English champions, but he was on the bench against West Ham United in the Premier League on December 23 and for the FA Cup clash with Wigan Athletic on January 8.
There had been speculation surrounding a potential loan exit this month, with Man United keen for the defender to secure his first taste of senior action.
Stockport have won the race for his signature, and Bennett could make his debut for the club against Notts County on Saturday, providing that the fixture goes ahead, with a pitch inspection set to take place in the morning to determine whether the surface, which is frozen in parts, is playable.
"Manchester United defender Rhys Bennett will spend the rest of the season at nearby Stockport County," read a statement on Man United's official website, confirming the short-term move.
"The young centre-back has completed the first loan move of his career, and will look to gain a first taste of senior football when representing a team riding high as League Two leaders."
Bennett, who signed a new contract with Man United last summer, captained the Under-18s to success in the FA Youth Cup in 2022, netting against Nottingham Forest in the final.
Stockport head coach Dave Challinor told the club's official website: "Rhys is someone we know and who knows us. He spent a couple of months with us last season as part of an arrangement we had with Man United to get some younger players into our environment to train.
"It's fair to say he made a lasting impression on all of the staff not just in terms of his ability, but as a character and personality in being mature and having an understanding of the game.
"When the opportunity came to bring him back in, especially due to our current situation, it was something we were all keen to do and it's great to have him back with us."
Meanwhile, director of football Simon Wilson added: "This is a good example of how clubs can work effectively with each other. Rhys trained with us last season for a month on work experience, which was part of a wider initiative by Manchester United to give their players some preparation for a loan in senior football.
"The feedback all round from that was excellent, Rhys has kicked on since with United's first-team but is now available for loan and having had that initial exposure to each other it was an easy win for all parties.
"He gives us good depth across defensive positions. The previous time together gives us all a head start and I'm sure Rhys will settle quickly and contribute to our important remaining games this season."
Bennett, who has been with Man United since the age of nine, will wear the number 26 shirt for Stockport.