Aye.
I've been keeping an injury log for 2 and a bit seasons, and I roughly average an injury every 2nd day (4 to date this season), though that rate goes up if I start power-training. That's managable with a 22-man squad with plenty of dual-role players.
I keep my medical and pitch facilities as developed as possible, and avoiding having players take the field with stamina < 90% or morale <80%, which seems to help.