Greenfield Police Chief Bradley Wentlandt says a suspect was "put down" during the exchange and that the shooter was down on the scene, adding that it was unknown around 1 p.m. Sunday if there were additional shooters inside the temple.
Wentlandt said during a briefing to reporters that the officer was shot multiple times and was transported to a hospital. He said the officer is expected to survive.
Police and witnesses described a chaotic situation with an unknown number of victims, suspects and possible hostages, as witnesses outside of the temple said people inside with whom they have spoken were describing a hostage situation.
Oak Creek Police Department dispatcher Stephanie Uljanec says the shooting took place Sunday morning at the Sikh Temple of Wisconsin but she doesn't know how many people are shot or if there are fatalities.
A spokeswoman for Froedert Hospital, the main trauma center in the Milwaukee area, says doctors there are treating three victims of the shooting.
Froederdt Hospital spokeswoman Carolyn Bellin says the three victims are all men. She did not have their identities or know why they were at the temple Sunday morning when the shootings occurred.
Belliin says one of the men is in the operating room, another is in a surgical intensive care unit and the third is being evaluated in the emergency room.
Belliin says the hospital is a level-one trauma center and is prepared to receive more patients from the shooting, but does not know if more will be on the way.
Sukhwindar Nagr, of Racine, said he called his brother-in-law's phone and a priest at the temple answered and told him that his brother-in-law had been shot, along with three priests. The priest also said women and children were hiding in the temple, Nagr said.
Reports around noon Sunday indicated various possible numbers of people injured, ranging from four to 30. Some reports indicated that people were seen on the ground in or near the temple.
At 12:10 p.m., the Milwaukee Journal Sentinel newspaper reported they were receiving reports of 20 to 30 injuries.
There were more than a dozen ambulances parked outside the temple, and police corralled media and a handful of bystanders to an area near the temple.
Oak Creek is south of Milwaukee along Lake Michigan.
Wentlandt says that the first 911 call came in around 10:25 a.m. Central time and was "unintelligible." He said that reports of a shooting at the temple came in soon after, and authorities responded to the scene.
The Associated Press contributed to this report.