The Dutchman joined United in 2020 from Ajax but has not featured regularly for the club. He has made only two Premier League starts for United since returning from a loan spell at Everton in 2022.
After missing the first half of 2023 due to a ligament injury, he has appeared only once in the league this season as a late substitute.
"Van de Beek will be pushing for more playing time in Germany," United said in a statement.
"Eintracht Frankfurt are currently sixth in the Bundesliga and face a UEFA Europa Conference League play-off with Union Saint-Gilloise of Belgium in February."