Pellistri is yet to make a first senior appearance for United since joining from Penarol in a €10m deal in October.
The 19-year-old's representatives Eqipo TMA announced late on Thursday night that he had returned a positive test for the virus.
Solskjaer confirmed that news on Friday and but eased concerns about a wider outbreak at United, insisting that Pellistri had not been training with the first-team squad.
“I think we've done well to follow the protocols as we have, we've had the odd case and Facundo Pellistri got a positive,” Solskjaer said.
"He reported that on his Twitter. We don't normally comment on who they are but Facundo is well and hopefully he'll be back with us soon.
“He's been with the reserves and 23s and wasn't really in our group over Christmas. Apart from that, we have a full and fit squad.”
Pellistri’s agency said that the 19-year-old is “doing the corresponding quarantine at home, without symptoms and complying with the physical care indicated by his club”.
"We appreciate the messages received in the last hour. Soon he will be training again with his team-mates," the statement added.
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