Joyner's backup, Cody Davis, didn't participate in Friday's practice because of a sore quad and is listed as questionable.
McVay added the Rams are "optimistic" about Davis, but his availability nonetheless remains uncertain.
Joyner, however, is a major loss. The fourth-year pro out of Florida State moved to safety this year after excelling as a slot corner and has been playing both positions for defensive coordinator Wade Phillips.
Pro Football Focus graded Joyner fourth among 80 safeties through the first three weeks.
"Very versatile, but he's also such a great competitor," McVay said. "The effort, the energy that he plays with, snap in and snap out -- I think that raises the level of play with the guys around him. You feel him when you watch the tape."
Center John Sullivan also is questionable for Sunday's game because of a hip injury.