Mata was not included in the match day squad for Thursday night's Europa League goalless draw with Real Sociedad, despite appearing as a late subsitute in Sunday's win over Newcastle.
Solskjaer confirmed after the final whistle that Mata was injured and that he is likely to be sidelined for a few weeks, though did not specify the nature of the issue.
"Juan unfortunately will be out for a couple of weeks," Solskjaer said. "He missed tonight, yeah."
Mata has only made 12 appearances and eight starts for United this season but adds to a growing list of absentees.
Edinson Cavani, Donny van de Beek and Scott McTominay are all doubts for Sunday's trip to Stamford Bridge, while Paul Pogba is not ready to return from a thigh injury.
"We hope that they can be available for the weekend, but I’m not sure," Solskjaer said regarding Cavani, Van de Beek and McTominay. "Paul is still out for a few weeks unfortunately.”
Daniel James was forced off midway through the second half of Thursday's draw with la Real carrying an injury which will be assessed.
“He felt a tweak," Solskjaer said. "With the intensity he works at he felt something, so we hope it’s not really serious. We’ll have to check on him."
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