A Stacy Wiegman, PharmD, Pharmacy, answered. Tobradex eye ointment is a combination of two medications in an ointment that is applied directly to the eye to treat bacterial infection and the associated inflammation.The names of the active ingredients are tobramycin, an antibiotic, and dexamethasone, a steroid. Stacy Wiegman, PharmD, Pharmacy, answered. Tobradex eye ointment is a combination of two medications in an ointment that is applied directly to the eye to treat bacterial infection and the associated inflammation.