McKinnon suffered a right calf strain in Sunday's practice.
"The good news is, it's not going to be long term. The bad news is, it's going to take him up to Week 1, our opener, so his opportunity to get more in rhythm in our system, that kind of goes out the door," Lynch told KNBR 680. "But he's played a lot of football, and we play a lot of football in the offseason, OTAs and all that, so we're going to have to trust that he's going to be ready."
"We don't expect to see him until that Week 1 and are hopeful that he heals in due time to be ready for that," Lynch said of McKinnon.
McKinnon, who signed a four-year, $30 million contract with the 49ers in the offseason, suffered his injury a few days after backup Matt Breida left last week's preseason opener with a separated shoulder. Breida is expected to miss the rest of the preseason but be ready for Week 1.
On Tuesday, the 49ers signed running back Alfred Morris to a one-year contract.
The 49ers also announced that they had placed safety Terrell Williams Jr. on injured reserve with a leg injury and signed defensive back Dexter McCoil to a one-year deal.