The shooting happened at about 2:30 p.m., and police were investigating whether the shooter fired from a nearby rooftop where shell casings were discovered.
A 34-year-old woman, Zurana Horton, who had hovered over students to protect them as shots were fired, was struck in the face and chest and was pronounced dead at the scene. A 31-year-old woman was hit in an arm and the chest and was hospitalized.
The 11-year-old girl, a sixth-grader at the Brooklyn school, injured one of her arms and had a graze wound on her cheek. None of the victims was related, police said.
The victims were on a street corner at the back of the elementary school when the gunshots rang out, Department of Education spokeswoman Margie Feinberg said.
It's unclear how many shots were fired. Seven shell casings from a 9mm semi-automatic pistol were found on the nearby rooftop. Five other shell casings were found on the sidewalk in the front of that building, police said.
Three men were seen fleeing the scene, and police were questioning at least one person. The shooter was being sought, and police offered a $12,000 reward for information in the case, New York Police Department spokesman Paul Browne said.
The school's neighborhood, Brownsville, is located in southeastern Brooklyn and is among the most crime-plagued in the city. It's also where tens of thousands of people, mostly black and Hispanic men, are stopped, questioned and frisked annually by police. Critics say the men are being unfairly targeted, and only about 10 percent of stops city-wide result in arrest.
Police say the tactic is a necessary crime-fighting tool that helps get illegal guns off the streets.
"Police conduct stops of individuals evincing suspicious behavior in areas where shootings occur in order to prevent, or at least lower, the frequency of tragedies like the one in Brownsville today," Browne said.