Calvillo suffered a concussion in a 24-21 loss to the Saskatchewan Roughriders on Aug. 17 and hasn't practised or played since.
Montreal is 2-0 in his absence, thanks to rookie Tanner Marsh.
Marsh came off the bench to lead Montreal to a 39-38 win over the B.C. Lions on Aug. 22.
The 23-year-old Texan made a successful debut as a CFL starter Tuesday night, completing 18-of-27 passes for 309 yards and a TD in a 20-9 road win over the Toronto Argonauts.
Marsh is expected to make the start Sunday when Montreal (4-5) hosts the Argos (5-4).
Calvillo, 41, is in his 20th CFL season and 16th with the Alouettes.
Montreal has nine regular-season games remaining, however the move doesn't mean Calvillo can't return to the lineup before the start of the CFL playoffs as clubs can pull two players off the nine-game injured list each season.