UPS Store hours vary depending on the location. Generally, they close between 6:00 p.m. and 7:00 p.m. on weekdays. On Saturdays, many stores shut down between 2:00 p.m. and 4:00 p.m. Most UPS Stores do not open on Sundays. When it comes to UPS support hours, customer care is available from 8:00 a.m. to 8:00 p.m. EST, Monday through Friday.