Chabahar, near Iran's border with Pakistan on the Sea of Oman, is home to a newly built port and is an economic free zone.
"Iran will bring terrorists and their masters to justice", he wrote on Twitter.
"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.
Iran Foreign Minister Mohammad Javad Zarif condemned the attack and warned "terrorists" that they will be punished.
There was no immediate claim of responsiblity for the attack.
Washington has granted exceptions to some U.S. sanctions on Iran for the project.
Sistan-and-Baluchestan - which borders Pakistan - has suffered several terror attacks targeting both civilians and security forces over the past years.
India is developing the Chabahar port along with Iran and Afghanistan. Later reports dismissed that the police chief of Chabahar was among the casualties.
The official, however, emphasized that people in this area of Iran stand firmly united, and will foil all enemy plots.
The attack comes as Iran's economy reels in the wake of the U.S.re-imposing sanctions lifted by Tehran's nuclear deal with world powers. Authorities did not identify who was behind the attack, but Iranian media initially blamed the attack on Ansar al-Furqan, a Sunni jihadi group.
An official said that "the terrorist who carried out the attack was killed".
In June past year, IS militants attacked parliament and the shrine of Ayatollah Ruhollah Khomeini, the leader of the 1979 Islamic Revolution, killing at least 18 people and wounding more than 50.
In December 2010, at least 41 people were killed and 90 others were wounded following a suicide attack near a mosque in the city.
Terror attacks in Shiite Iran are rare, but militants have stepped up action in recent months.
The US, the Israeli regime and "the terrorist governments in the region that support them" feel desperate and angry over the "shameful defeat" they have suffered in their attempts to strip the Iranian nation of their independence and freedom, he said.