Rashford missed United's FA Cup loss to Leicester City with a foot issue and was ruled out of England's World Cup qualifiers against San Marino, Albania and Poland but the 23-year-old has returned to training.
"I don't know about Anthony, he didn't join in training this morning... but Marcus and Mason trained and hopefully they can get through that with no reaction," Solskjaer told reporters.
More good footwork from Rashford then drew Joe Willock into an ill-advised challenge inside the box and the on-loan Arsenal midfielder conceded a penalty.
Top English players including Liverpool captain Jordan Henderson and former international Karen Carney discussed online abuse and discrimination with government ministers last month.
Britain's Prince William, who is president of the English Football Association, on Sunday branded the racist abuse directed at footballers "despicable".