"Assailants armed with iron rods and machetes attacked people in a queue at Kinuni voters' registration centre," George Kizuguto, the police spokesman for Zanzibar township, said on Thursday.
He said nine people, including the officer, had been hospitalised as a result of the attack.
The incident, which took place on the outskirts of Zanzibar town on Wednesday, was the latest in a series of attacks related to the upcoming general elections that have polarised tense relations between the island's main political rivals.
Witnesses said the attackers were supporters of the ruling Chama Cha Mapindizi (CCM - Revolutionary Party) and the wounded - with the exception of the police officer - were members of the opposition Civic United Front (CUF).
The identities of those involved could not be independently confirmed. The attack comes a day after another group of armed men, allegedly CCM supporters, wounded three CUF party agents at a voter registration centre.
Witnesses to that incident on Tuesday said about 70 assailants disembarked from pickups and started hitting people in the Kinuni area of the island, which has a history of political violence.
"We are working on each incident carefully so that we can bring all the culprits to book"
Zanzibar's deputy director of criminal investigations
"They got off from the cars, came towards the queue and started beating up people who were at the place to register in the voters' book," one witness said on condition he not be named.
Zanzibar's Deputy Director of Criminal Investigations Ramadhani Kinyogo said police were looking into all the incidents and allegations of political motivation and would take necessary action.
"We are working on each incident carefully so that we can bring all the culprits to book," Kinyogo said.
Voter registration on Zanzibar was briefly suspended last week in an effort by election authorities to cool tensions that have flared since the beginning of March.
Opposition parties throughout Tanzania repeatedly say that the CCM has recruited armed youth, notably in Zanzibar, to intimidate voters from registering for the 30 October polls, but the ruling party denies the claims.