Howard was crocked in the recent FA Cup replay win over Oldham after a clash with Robbie Simpson - but still finished the game.
Blues boss Moyes - whose side follow today's sixth-round tie against Wigan with the visit of Manchester City - said: "Tim has broken two bones in his back and is out.
"He has two fractures but they are not the bones which are supporting anything. They are off the spine, they are not weight bearing.
"It just needs healing time. It is a question of whether he can cope with the pain. The bones will heal but it's not good.
"We're not sure how long he will be out because a keeper has to dive and hit the ground."