Police later identified the victim as Lamar Walters, 38, of Northeast Washington.
The homicide was the city’s fifth of the new year.
Two other victims later showed up on their own at hospitals, police said. Their wounds were described as non-life-threatening.
Police are searching for the gunman. The motive for the attack is under investigation, said Cmdr. William Fitzgerald, head of the police department’s Fifth District.
He said officers in recent months have targeted the area around the grocery store for increased anti-drug enforcement and have made several arrests for alleged drug dealing and possession.
A reward of up to $25,000 is being offered for any information that may lead to an arrest and conviction in the case, police said.
Dana Hedgpeth contributed to this report.