Varner said a fight between several people outside the apartment escalated into a shooting.
Johnson was not a target, Baker told reporters.
Neighbours told local media that they had heard as many as 40 gunshots.
Photos and videos showed the windows of Johnson's apartment riddled with bullets.
Portia Weatherspoon, Johnson's neighbour, told ABC affiliate WATN that she stepped outside after hearing one of Johnson's nephews yell that his uncle had been shot.
"When I went in the house, I found him shot," Weatherspoon said. "Me and my husband tried to do CPR."
It's unclear whether police have made an arrest. It's also unclear how many other people were in the apartment, but no one else has been injured.
Johnson's death was a blow to the small, tightknit agency of 35 officers. Varner said Johnson worked in the Forrest City Police Department's patrol division and had always been willing to take on more tasks, whether it was helping serve a search warrant or providing security at special events.
Varner said the agency has set up a GoFundMe campaign to raise funds to help the Johnson family.