IRNA, Iran's state news agency, said the attack took place at around 1900 local time (1430 GMT).
Sheikhi said a child was also shot in the stomach and was undergoing surgery.
Two campaign workers sustained arm, stomach and shoulder wounds and were taken to hospital, he said.
"The men ran away, but the police chased and arrested them," Sheikhi said.
Zahedan is the regional capital of the Sistan-Baluchestan province which borders Pakistan and Afghanistan.
Iran goes to the polls in presidential elections on June 12.