City police said they had taken into custody a man they suspect was the shooter and were looking for two women who left the scene -- one woman looking for her tax refund and another who was a witness, the Detroit Free Press reported.
One of the gunshot victims was in critical condition, while the other three were listed in serious condition, the newspaper said.
The shooting started shortly after 3:30 p.m. in the office of Tax City Tax Service and spilled out into the street. Police said a passerby flagged down an officer and pointed out the alleged gunman, who was arrested nearby. The gun used in the shooting was recovered, police said.
"The suspect and two other individuals came to the tax location and one person was requesting a payment," Detroit Police Chief James Craig said. "The payment wasn't ready. There was a physical altercation."