The suspect, who was not identified, was being questioned on the third floor of the building when the shooting happened, said Police Chief Rebecca Coleman. Police did not release any details on the sequence of what happened but scheduled a news conference for later Thursday night.
The officer was identified as Eric Smith, a homicide detective.
Jackson City Councilman Chokwe Lumumba was in police headquarters with the mayor and said Smith was shot by the suspect. He did not know how the suspect ended up dead.
"I understand there may have been more than one police officer in the room," Lumumba said outside the police building.
The headquarters was blocked off and surrounded by crime tape. Law enforcement and Jackson city officials rushed to the scene.
City spokesman Chris Mims said the Mississippi Bureau of Investigation will take over the investigation, which is standard procedure.
"We're asking for everybody's patience, we will be releasing information as soon as we have it," he said. "This is an extraordinarily tragic situation."
At least 30 Jackson Police and Hines County Sheriff's office cars were haphazardly parked across multiple, major downtown Jackson streets.
Lumumba, who is a lawyer, said Smith is rather new to being a homicide detective and that he met Smith in the late 1990s. The then-officer had testified on some of Lumumba's cases.
"I had great respect for his work and his integrity," Lumumba said. He added that Smith's stepson had played basketball on an Amateur Athletic Union team that Lumumba worked with.
"Eric helped take young men all over the country," the councilman said. "He's a real man in every sense of the word."
Mayor Harvey Johnson, Jr. also addressed the officer's death.
"Detective Smith was an excellent officer in all respects," the mayor said. "I want everyone to keep the Smith family in their prayers and in their thoughts."
Lumumba said that Smith was married and had another son.
A monument outside police headquarters lists 14 officers killed in the line of duty before today.