Chabahar is located in Sistan-Baluchistan, an impoverished region bordering Pakistan whose mainly Sunni Muslim population says it suffers discrimination from Iran's Shia authorities.
The Sunni Muslim rebel group Jundollah carried out a series of attacks in the region from 2005, but has been far less active since its leader was arrested and executed in 2010.
Other groups have taken its place but they are smaller and less organised, experts say.
"This morning, this suicide operative wanted to enter the police headquarters and commit a terrorist act while wearing a suicide vest and carrying a grenade," the Mehr news agency quoted the governor of Chabahar, Iraj Heydari, as saying.
The attacker shot at security forces, wounding one of them, before being killed, Heydari said. The report made no mention of the identity or motive of the attacker.
In October a suicide bomber killed two guards as he blew himself up outside a mosque in the same region after being prevented from reaching worshippers inside.
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