Peters was leaving a graduation party in the Lower Ninth Ward when she was shot to death.
Two other victims were wounded in the shooting, including an 18- and 19-year-old male.
Brown was booked on one count of second-degree murder and two counts of attempted second-degree murder.
This is still an active investigation.
NOPD Superintendent Shaun Ferguson addressed the arrest during a briefing on Tuesday afternoon to update the community on a recent spate of violent crimes plaguing the city.
“I would like to thank VOWS (Violent Offender Warrant Squad),” said Chief Ferguson. “I would like to thank our partners at the US Marshals. But I would also like to thank Sheriff Jimmy Pohlmann and his team at the St. Bernard Sheriff’s Office.
“We could not have solved this case without them.”