Kristof Terreur of HLN reported there was no ligament damage or fractures and that Lukaku will undergo an individual program in the coming days.
The star striker is expected to lead the Belgian attack in the 2018 FIFA World Cup qualifiers against Bosnia and Herzegovina and Cyprus. The Red Devils have already qualified.
The Belgium international moved to Old Trafford during the summer of 2017 after a productive spell with Everton. According to Dawson, the Red Devils paid a hefty fee for Lukaku, with bonuses potentially taking the price tag to about £90 million.
There's little doubt the 24-year-old is worth such a sum, given his excellent scoring record in the Premier League. Last season, he bagged 25 goals for the Toffees.
At United, he was brought in to replace veteran star Zlatan Ibrahimovic, who got injured late in the season and didn't initially have his contract renewed. The Swede has since rejoined the club.
Consistency can be an issue for Lukaku at times, and his tendency to search for open space and slide outside means he isn't as great at holding up the ball inside the box as fans would like. But the forward is a deadly finisher when on form, and United are undoubtedly a better team with the Belgian.
For now, the issue does not appear too serious, but the club will monitor the situation nonetheless and hope Lukaku is good to go when he returns from the international break.
Marouane Fellaini also sat out Monday's training session.