Chabahar governor Rahmdel Bameri said many people were also wounded in the morning car bombing.
"The explosion was very strong and broke the glass of many buildings close by," Bameri told state television.
Many nearby shop owners and civilian passers-by, including women and children, were severely wounded, he added.
Chabahar lies in Sistan-Baluchistan province some 100 kilometres (60 miles) west of the Pakistan border.
The province has a large, mainly Sunni Muslim ethnic Baluchi community which straddles the border and has long been a flashpoint, with Pakistan-based Baluchi separatists and jihadists carrying out cross-border attacks targeting the Shiite authorities.
The province's deputy governor in charge of security, Mohammad Hadi Marashi, said multiple assailants took part in Thursday's attack.
"The terrorists tried to enter Chabahar police headquarters but they were prevented by the guards and they detonated the car bomb," he said.
Chabahar has a deep-water port on the Gulf of Oman and with Indian assistance Iran has been developing it as a a major energy and freight hub between Central Asia and India, bypassing Pakistan.
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