Melbourne Police tweeted that the "shooter is contained" and that officers were clearing the Melbourne Square Mall store by store.
It wasn't immediately clear whether the suspect was dead or one of the injured people taken to a hospital, Cmdr Vince Pryce said.
The shooting occurred before the mall opened at 10 am local time. Mall officials posted a statement to Facebook saying the mall was closed until further notice as police investigate.
Local television news broadcasts showed yellow police tape stretched across a mall entrance and the parking lot.
"We had just gotten our food to sit down by Starbucks and Chik-fil-A, and you just hear the 'pop, pop, pop, pop, pop, pop, pop,' and you just drop everything and your body just makes you run," Evans told Florida Today.