The Tasnim news agency said there were reports that women and children were among the injured.
"The terrorists exploded a vehicle carrying explosives at the gate of the [police] headquarters", Bameri was quoted as saying by the official government news agency IRNA.
In a communique, the Sunni jihadist group Ansar al-Furqan claimed responsibility for the attack, according to the Washington-based SITE Intelligence Group, which monitors extremist activity online. A little-known Sunni jihadist group claimed responsibility for the attack, which Iran's foreign minister accused of being "foreign-backed".
Suicide bombings are rare in Iran, but Sunni militant groups have carried out several attacks on Iranian security forces in the Sistan-Baluchestan province in recent years.
In October, the separatist Jaish al-Adl (Army of Justice) group kidnapped 12 Iranian border guards in the remote province, five of whom have since been released.
Last year, in the first deadly assault claimed by Islamic State in Tehran, 18 people were killed at the parliament and mausoleum of Ayatollah Ruhollah Khomeini, founder of the Islamic Republic. Iran's supreme leader, Ayatollah Ali Khamenei, blamed Saudi Arabia and the United Arab Emirates for the attack, allegations denied by both countries. "As we've made clear in the past, such crimes won't go unpunished".
"Terrorists attacked the police post in Chabahar with an explosives-laden vehicle", he said.
"In 2010, our security services intercepted & captured extremists en route from UAE".
Meanwhile, Iranian Foreign Minister Mohammad Javad Zarif claimed that those behind the attack were backed by foreign countries and would be brought to justice.
Chabahar, on Iran's south-eastern coast near the border with Pakistan, is home to a recently built port and is an "economic free zone".
Chabahar has a deep-water port on the Gulf of Oman and with Indian assistance Iran has been developing it as a major energy and freight hub between Central Asia and India, bypassing Pakistan.
It said India condemned the "despicable terror" attack. "There can be no justification for any act of terror", an MEA statement said.