Shaw had to be substituted in the first half of Saturday's 1-0 home loss to Aston Villa, having seemingly picked up a muscular problem, while Maguire was forced off in the second period following a kick to his calf.
Solskjaer is unclear of the extent of the damage at this stage, but the Man United manager has admitted that the pair are unlikely to be available for the team's next game against Villarreal.
"At the moment they don't look okay for Wednesday but let's see," Solskjaer told BBC Sport.
Man United have now lost three of their last four matches in all competitions and back-to-back fixtures at home, having also been beaten 1-0 by West Ham United in the EFL Cup last week. body check tags ::