The 23-year-old forward has earned huge praise for his off-field work around food poverty among children.
But Solskjaer said: "He is coming into the best age for a footballer and he's got a challenge on his hands here at Manchester United - and has a challenge on his hands to play for England."
Rashford became an MBE in 2020 and this month received an honorary doctorate from the University of Manchester.
However, Solskjaer says the forward must keep his focus on his day-job.
The manager, though, does not feel Rashford's activities away from the pitch have impacted his on-field performances.
"Marcus has done some remarkable and fantastic things," added Solskjaer as Rashford prepares to return from the shoulder operation he had following Euro 2020.
"But now he maybe needs to prioritise his football."
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