The official CNA news agency said five firefighters, four members of the Greek Cypriot National Guard and two sailors were killed, citing military sources. State television said at least 12 people were killed.
A defence ministry spokesman interviewed by public radio confirmed that there were deaths but declined to give a figure.
The radio said at least 30 people were also injured in the explosions which it said struck among weapons seized from an Iranian shipment aboard a Cypriot-flagged vessel in 2009.
It said that it was the worst peace-time military accident in the island's history. Witnesses told the radio of a scene of devastation in the adjacent fishing village whose seafront restaurants are popular with the many tourists who frequent the resort island.
Cars, houses and restaurants alike suffered massive damage from the force of the blasts, the witnesses said.
Commerce Minister Antonis Paschalides told the radio it was a "tragedy of Biblical dimensions." The radio said that the fire brigade were called to a blaze near the base at 4:24 am (0654 IST) and that the explosions followed at 5:50 am (0820 IST).
Wildfires are a frequent problem in Cyprus in the tinder-dry conditions created by the searing summer heat.