The blaze Saturday caused an estimated $1 million in damage and forced 25 people from their homes.
The fire was reported at 6:19 a-m and was extinguished two hours later. No one was injured.
Lieutenant Fred Varnell said it has not been determined how the arsonist started the fire and no arrests have been made.
Four apartments were destroyed and four damaged in the 16-unit building. Residents were offered vacant apartments elsewhere in the complex.