Last Season I had this problem. I had between one injury per day up to three in a single match. At the peak I had 20+ injuries in a single week. More than three per day in average. It has slowed down now but it should be generally reduced. I don´t think a team has ever had like 80-90% of injured players in any league.

Towards the aforementioned propositions:
-I have always built Ambulance and green first in my stadium.
-I Never play hard tackling.
-Had already stopped training completely.
-Never played out of position.
-Morale at maximum.
-Always trained moderate in general, even before stopping it completely.
-Never trained a player below 80% fitness.
-Fitness was always above 90% to matches.
-Injury prone players? It was the whole team! The same team that did well in previous seasons.

This injury stuff is a real killer. It´s neither fair nor fun. Fix injuries!