Reuven Rahamim was shot to death in the Thursday attack at Accent Signage Systems Inc. in a residential neighborhood on the north side of the city, Chad Blumenfield said in a statement.
An "incredibly proud husband, son, father and grandfather, has passed away in a senseless act of violence," Blumenfield said. "Other members of the Accent family tragically lost their lives as well, and we mourn their loss." He provided no details.
Police spokesman Sgt. Stephen McCarty said the gunman also injured four people in the attack before apparently shooting himself. Police have not released the shooter's identity or a motive.
A police summary of the shooting issued early Friday described a chaotic scene, with multiple 911 calls from the business and a caller saying someone had been shot inside. When police arrived, they found four people already dead.
Of the wounded, John Souter's condition was upgraded from critical to serious as of Friday morning and Eric Rivers remained in critical condition, according to Christine Hill, a spokeswoman for the Hennepin County Medical Center where they were being treated. She had no information on the condition of a third man earlier listed in critical condition.
A fourth person injured has been treated and released, Hill said Friday.
Police spokesman Steve McCarty said police late Thursday searched a house where the suspected gunman had lived but found "nothing that we know of." He declined to confirm a newspaper report that named the suspect.
Accent spokeswoman Wendy Khabie declined comment Friday morning.
Minnesota Gov. Mark Dayton expressed his condolences to the families and friends of those involved.
"I deplore this senseless violence. There is no place for it anywhere in Minnesota," Dayton said.
Dozens of police squad cars and SWAT officers swarmed the Bryn Mawr neighborhood where the business is located, after an employee called 911 around 4:30 p.m. to say shots had been fired. The first officers on the scene evacuated people from the business that makes interior signage and closed off several blocks.
Marques Jones, 18, of Minneapolis, said he was outside a building down the street having his high school senior pictures taken when he and his photographer heard gunfire that sounded close.
"We heard about four to five gunshots," Jones said. "We were shocked at what happened and we just looked at each other. We all just took off running to our vehicles."
Associated Press writers Doug Glass and Jeff Baenen in Minneapolis, and Barbara Rodriguez, Erin Gartner and M. David Nichols in Chicago contributed to this report.