The master bath currently has a separate shower and tub. I would like to remove the shower and reclaim the space as a closet. How should I cap off the drain after removing the shower?

If it's plastic, simply cap it off below the floor with a glue type schedule 40 cap.

And you'll want to do the same for the supply and mixer valve. If its not plastic just let us know and we'll fix you right up. No need to rip out walls if its going to be a closet. I'd screw 3/8" plywood over the wall with the fixtures removed and paint it. That way you can always get back inside in case some goes south on you inside the wall.