Depay was substituted at half-time during Monday's (AEDT) Ligue 1 defeat at home to Rennes, having initially been hurt in a tussle with Hamari Traore.
The forward sustained a suspected anterior cruciate ligament injury to his left knee that could rule him out of action for several months.
Depay now faces a battle to return in time to feature for Netherlands at Euro 2020.
"We expect Memphis' injury to be quite serious," Juninho told OL TV.
"We expect it to keep him out for the rest of the season. He's our captain and I'm sad for him."
Depay's injury came after they had also lost Jeff Reine-Adelaide to a suspected meniscus problem, with reports suggesting he could be out for around four months.
The former Manchester United man has scored nine goals and assisted a further two in 13 Ligue 1 appearances this season, as well as netting five times in five Champions League games.
Rennes moved up to fourth in the Ligue 1 table thanks to a 1-0 win earned by a late goal scored by 17-year-old Eduardo Camavinga, with Lyon sitting eighth after 18 games.
Lyon coach Rudi Garcia said: "I'm not happy with the results or the performances. The evening is made worse by the fact that we lost Reine-Adelaide and Depay to injury."