Head coach Scott Milanovich provided the injury update at the team's practice session at York University.
Durie, from Mississauga, Ont., is expected to be out of the lineup for six weeks. It wasn't immediately clear how long Emry will be out.
In two games this season, Durie has 10 catches for 130 yards and two rushes for 18 yards. He suffered the injury late in Saturday's 48-15 home win over Saskatchewan.
Durie had 92 catches last season for 986 yards.
Emry, a veteran linebacker in his first season with Toronto, has six tackles this season. He was also hurt in Saturday's game.
The Richmond, B.C., native had 46 tackles, two sacks and two interceptions last season with Montreal.
The Argonauts are tied for first place in the CFL East Division after splitting their first two games.