The injury-prone Ivory Coast international was an unused substitute for the 4-1 win over Newcastle United last weekend.
Bailly also didn’t make the squad for the Red Devils’ 2-1 Champions League victory against Paris Saint-Germain on Tuesday night, and speaking after the game, Solskjaer confirmed the centre-back’s injury.
‘Eric has a muscle injury, we think maybe three or four weeks, maybe after the international break he’ll be back,’ the Norwegian boss said.
United produced an impressive performance against PSG at the Parc des Princes without Bailly and captain Harry Maguire, who also missed out through injury.
Bruno Fernandes and Marcus Rashford got the goals for the Red Devils, but it was Axel Tuanzebe that caught the eye for his solid display in defence.
Asked if Tuanzebe’s performance has made him undroppable, the Red Devils legend told BT Sport: ‘Yes. Ole has just said it’s two of the best two strikers in the world, he snuffed out danger many a time today.
‘You have to reward performances like that. He’s had a hard time with injuries – first game in 10 months – to come in and play like that, from in out of the cold, you deserve to be rewarded.
‘This is where Man United have struggled in the last six to 12 months, in them areas chasing players down the channels, they can’t stay with them and then obviously that opens up the back four or back three. But he was smelling danger.’