Aguero suffered a right calf injury in Sunday's training session, before Messi gave a farewell speech at the Camp Nou after Barca were unable to sign him to a new contract. Messi is expected to join Paris Saint-Germain as a free agent.
The ex-Manchester City forward underwent a scan on Monday morning and Barca announced Aguero will be out for up to 10 weeks, though club sources have told ESPN they are hopeful he will be back in eight.
Barca coach Ronald Koeman described Aguero's injury on Sunday as a "setback."
"It's a pity he got injured and could not play 30 minutes at the Gamper," Koeman said. "It's a setback as he was training and can bring a lot to the team with his quality up front."
Martin Braithwaite, who started on Sunday, was expected to be on his way out of the Camp Nou after the Danish striker failed to gain regular playing time last season, but he is now likely to remain.
Depay scored his team's opener against Juventus and assisted Braithwaite for Barca's second goal.
"We've signed players like Memphis that are very effective," Koeman said. "Of course, it's always important to have the best, but if it can't be, we will not change our ideas or way of playing.
"There are other players that can occupy that position. We've seen a good Griezmann. We'll need to step up and improve because we won't have Leo's goals."