The gunfire erupted along the parade route on St. Charles Avenue and 2nd Street. The toddler was not hurt seriously, KATC-TV in Lafayette, La., reported.
Two suspects were in custody, the TV station said.
The day's celebrations brought out huge crowds -- organizers said they hoped to match last year's 750,000 -- who were enjoying themselves before the violence.
"We love it, we are having so much fun, we're so tired," Pat Kirby told KATC.
Mardi Gras is known for the outrageous behavior and costumes of the revelers and parade participants alike.
"It's nice to be king for a day," said a New Orleans man dressed in a cape and crown.
Tara Dzialak and her family lined the route in pirate costumes.
"We've always heard that everybody dresses up for Mardi Gras and a whole group of us decided this is what we're gonna do," Dzialak said.
One man's outfit was covered in men's ties, two women used old doubloons to fashion skirts.
"You've got to do something with all the stuff you collect right? So here it is," said Elizabeth Yost-Hammer of New Orleans.