The incident at the Riverchase Galleria in Hoover started with a physical altercation between an 18-year-old and the 21-year-old gunman, police said.
A 12-year-old girl was also struck and injured, Rector said, but it's unclear by whom.
"Oh, they shooting in this house", a woman screams as the shots ring out.
That individual, an 18-year-old, was then confronted by two Hoover police officers and was shot dead at the scene, the local NBC news affiliate reported.
The girl had a single gunshot wound and has gone through surgery and "does not have life-threatening injuries", Rector told CNN.
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The gunfire erupted just after 9:50 p.m. Thanksgiving Day at Riverchase Galleria in the town of Hoover, about 10 miles from Birmingham, local reports said.
"This was my first Black Friday, I knew it would be insane, just not this insane", she said.
The injured 18-year-old was in serious condition when an ambulance took him to the hospital, police said.
The officer involved has been placed on administrative leave while the Jefferson County Sheriff's Office investigates the incident, police said.
"While there is no current danger to our community, we will remain closed until further notice", Riverside Galleria said in a statement.
The city followed up with a tweet at 12:09 a.m.to thank the police officers and paramedics who responded to the scene, saying, "Our HPD officers acted heroically and professionally tonight". We are working closely with the Hoover Police Department. I'm so shaky right now I'm sorry if I don't make any sense.