Can you see under the closet floor from a basement? If so you should be able to see the ducting that supplies that vent. Follow it back to the main trunk line and you might find a damper. Close it and/or disconnect this run from the main trunk line by purchasing a cap or screw a piece of sheet metal over the hole.

If you can't access underneath, take the vent register off and with a mirror or flashlight look inside and see if you see a damper. Sometimes they are near the register. Maybe you can close it from there. Some air will pass so you might want to disconnect the run as I described.