Madison Police spokesman Joel DeSpain told the paper that one of the victims was transported to a local hospital with leg injuries.
"We don't believe this is related to terrorism," DeSpain said, "This was obviously not a mass shooting. This is an incident where we had young people ... who were in a dispute and one of them pulled out a firearm and unfortunately shot a gun in the middle of East Towne Mall on the busiest shopping day of the year."
The mall ordered stores to close and evacuate in the aftermath of the incident. The mall was secured shortly before 3:45 p.m. local time, police said.
Authorities arrived on scene shortly after reports of multiple shots being fired around 2:50 p.m. local time, between the Boston and Hallmark stores inside the mall, the paper reported.
A Gordman's department store employee, Lester Callahan, told the paper that mall shoppers ran into his store to hide in the immediate aftermath of the incident.
The mall soon gave a directive to Callahan's store to close and evacuate, he said.
A notice posted on the mall's website says: "The mall is temporarily closed due to a safety concern."
East Towne Mall is an 840,000-square-foot shopping center with 110 specialty retailers, according to its website.
The Associated Press contributed to this report.