Pogba twisted his ankle in the 1-1 draw at Southampton two weeks ago and did not play for France in their two matches during the international break.
Pogba 'has an ankle problem' following United's 1-1 draw at Southampton on Saturday.
United supporters have promised to show their backing for Pogba when the France midfielder returns to Old Trafford for the Premier League meeting with Crystal Palace on Saturday.
Pogba was targeted after his penalty was saved in United's 1-1 draw at Wolves on Monday just days after Chelsea striker Tammy Abraham suffered similar abuse.
Marcus Rashford revealed Paul Pogba had said he wanted to take the kick and, publicly at least, the England striker had no problem with that.
At an average of 24 years and 173 days, Solskjaer had picked United's youngest Premier League starting line-up since the final day of the 2016-17 campaign.
In the battle between two former club legends in the dugout, it was Solskjaer who came out on top in Lampard's managerial debut in the Premier League.
Paul Pogba was missing from the Manchester United squad for the pre-season penalty shootout win over AC Milan in Cardiff.
Madrid have had a bad start to their season, as they have already lost their four pre-season games. They were able to win just one match against Arsenal at the Intercontinental Champions Cup.
Pogba's publicly stated wish to leave and his tepid displays at the end of last season have infuriated many United supporters.
The Frenchman has publicly stated his wish for a "new challenge," amidst interest from Real Madrid.
Anthony Martial rounded out a spectacular performance in the 68th minute by converting a penalty after Tahith Chong was taken down in the box.
An under-pressure United struggled in their pre-season opener against a weakened Perth Glory, who won Australia's A-League Premiers Plate last season.
Uncertainty has also surrounded David de Gea's future but Solskjaer said he was optimistic about the goalkeeper remaining at Old Trafford, despite only one year remaining on his contract.
The 26-year-old World Cup-winner's future has overshadowed United's pre-season tour since they arrived in Perth on Monday.