The water heater in my apt is leaking from a 1" copper pipe on the top of the unit. Is there a way to just shut it off do I don't have to deal with the water spillage on the floor?

Is it the cold in or hot out and where is the leak?

If you just want to stop the leak temporarily shut down the cold line feeding the heater. This might be plumbed in a way the whole apartment will lose hot and cold water. Do you own this unit.