De Gea returned home to Spain to be with his girlfriend at the birth of Yanay, with the United keeper having posted a picture on his Twitter feed, announcing the safe arrival.
Dean Henderson will be in goal for Sunday's Manchester derby and may keep the position until the international break, during De Gea's enforced absence.
"It's a fantastic day for David, of course," said Solskjaer. "When you become a dad that's the best possible feeling you could have and the ones lucky enough to have that feeling know.
"We will give him the time he needs, he has to go home and, in the old world, you go back a day, come back, but with the quarantine it's a different world.
"When David said he wanted to go and be there to support his girlfriend, it's not even a decision to make. Dean came in and played well, and he's ready. I'll give David the time he needs.
"As soon as David travels back, we just have to follow the Government rules, I expect him to be available very soon.
"We want our players back as soon as possible, but there's a human being in there and David was there for this fantastic day for him and his girlfriend.
"I don't know when he'll be back, but it won't be long before he comes back. It was easy when I travelled back from the Euros, my son Noah was born on a Friday, we played Spain on Tuesday, travelled back Sunday.
"But this is the biggest occasion in any parents' lives. Dean did well against Palace and is looking forward to this City game as well."