Both players came off early in Saturday’s 1-0 Premier League win over Luton at Old Trafford, for which manager Erik ten Hag was without eight first-team players.
Hojlund, the striker signed for £72m, left the field towards the end of the game with a muscle problem, while midfielder Eriksen suffered a knee injury in the first half.
United have now confirmed that Eriksen will be out for a month, with the club confident Hojlund will be able to make a return before the end of November.
Man Utd are already without Lisandro Martinez, Luke Shaw, Casemiro, Tyrell Malacia, Jonny Evans and Amad Diallo through injury.
Jadon Sancho remains exiled because of a disciplinary issue while Aaron-Wan Bissaka, just back from injury, missed Saturday’s game with illness.
Asked on Saturday about the injury to Hojlund, United’s top scorer this season, Ten Hag said: “In this moment I can’t say anything about it [Højlund’s injury] because I don’t know.
“We do an assessment but have to wait for 24 hours to see what the conclusion is. Give them, the medical [team], 24 hours to see what the problem is, if there is a problem.”
United are next in action on November 26 after the international break when they head to Everton in the league.
Games against Newcastle and Chelsea follow that with a trip to Liverpool on December 17.
