Hojlund was replaced in the latter stages of his side's clash with Luton Town before the international break due to a muscular strain.
The injury forced the 20-year-old to withdraw from the Denmark squad, and Man United said in a statement that the forward could be out until the latter stages of November.
Hojlund, who has scored five times for the club this season, will therefore need to be assessed before a decision is made on his involvement at Goodison Park.
Three Lions head coach Gareth Southgate played down the injury fears following his side's 2-0 win, telling reporters: "I think he [Rashford] is probably okay. We just thought given the nature of the collision it was a chance to get Cole [Palmer] into the game. I haven't assessed too much but I think he was okay when he came off."
Man United will want to conduct their own investigation, though, before determining whether their leading goalscorer from last season will be available for the game with Everton.
Onana had to be replaced in the latter stages of his country's 2-0 win over Mauritius, and he will now miss their next match against Libya on Tuesday.
Aaron Wan-Bissaka missed out against Luton before the international break through illness; he should have recovered in time for the Everton game, but Jadon Sancho is still not involved with the first team and will not feature.
Man United have won their last two league matches against Fulham and Luton, while they have been victorious in four of their last five in England's top flight to move into sixth position in the table.
The Red Devils will now be hoping that there are no further fitness issues to contend with during the latter stages of the November international break. body check tags ::