The attacker underwent surgery on a long-standing shoulder issue over the summer and has not yet been involved for the Red Devils during the 2021-22 campaign.
Rashford has recently been pictured in training, and there had been claims that the England international would be available for selection before the international break.
However, Solskjaer told Man United's official website that the 23-year-old attacker is unlikely to return until after the next set of international fixtures in October.
The Red Devils have three home matches against Aston Villa, Villarreal and Everton before returning to the field on October 16 with a trip to the King Power Stadium to take on Leicester.
Rashford, who featured for his country at Euro 2020 despite his injury issues, scored 21 goals and registered 15 assists in 57 appearances for Man United last term. body check tags ::