Abdiqani Adan, 29, who did not live in the building, died on Friday at the Hennepin County Medical Center in Minneapolis, according to the office.
Meanwhile, two survivors still in the hospital recounted jumping from windows to save themselves. Abdi Qobey, 59, was sitting in bed watching television early on New Year's Day when he heard a boom and saw the walls buckle.
"I see the smoke. I see already I'm going to suffocate if I stay one more minute," said Qobey. "I knew that if I stay, I'm not going to stay alive."
Turning to grab a few possessions, he couldn't see anything but the second-floor window. So he ran to it.
"I looked downstairs," he recalled. "I see one officer in the street. He says, 'Sir, the firefighters have not come yet. There's no other choice. You have to jump.'"
Qobey suffered fractures in both legs and a back injury but is glad to be alive, he said from his hospital bed in the Hennepin County Medical Center.
The explosion and fire broke out about 8:15 a.m. on Wednesday, immediately killing two people, injuring 14 and destroying the three-story apartment building. Nine people still were hospitalized Friday, including three in critical condition.
Ali Jama, 41, was visiting friends and sleeping in a second-floor apartment when he heard the loud boom. The windows shattered.
"When the windows were blown out, I took a look downstairs," said Jama, a truck driver from North Carolina. He tried to go down the stairs, but there was too much smoke. He kicked the rest of the window glass and sat in the window opening.
"I thought I might die," he said. "I prayed, but I thought I was dying."
He jumped and hit the ground two floors below. He broke both legs and several ribs. Two friends were also badly hurt when they jumped, he said, but they also survived.
One of the two people who didn't make it out of the building was identified Friday as Ahmed Farah Ali, a 57-year-old resident. His body was recovered Thursday.
A second body was recovered Friday. That person has not yet been identified.