I know this is an old topic but I ran into the similar problem in the career mode. Here is the solution:

1. In competition/season you will not be able to play if one of your players is injured. The injured player has a red cross next to its name (instead of a face). Substituting all the injured players with healthy ones will make it possible to play

2. In career mode, you need to have healthy players not only in the main team but also all the subs have to be healthy. So you need to put the injured players into reserves. To do so, you can go to your squad page. Notice that the bottom player has no number assign. This player is in reserve. Move the injured player into this position. If you have multiple players injured you have to move all of them in that way into reserves bringing healthy players in.

3. The third possibility is that the you changed tactics and the current tactic is not compatible with the players on the field. So you may need to adjust the players positions so they fit into them.

Hope that helps to anybody that had that issue... It took me a while to figure out how to do it in the career mode...