Yes. A residential garage door requires a minimum of 4 1/2” of headroom space. Your garage door system may need a low-headroom track system or a low-headroom-torsion rear-track system. For a garage door opener, you will need slightly more headroom (about 6 1/2” minimum).
Or you could always consider the LiftMaster wall-mount garage door openers. They mount on the wall next to the garage door, freeing up the space overhead and opening up the possibilities to maximize your garage space.