It happened just after 1 p.m. at the Foodtown on Allerton Avenue in the Allerton section.
Video of the attack shows the worker attempt to stop the pair, who appeared to be shoplifting, from leaving the store.
The video shows the worker and the male suspect tangled with each other before they both fall to the ground.
The worker held onto the suspect as he stood up to get away and that's when the man threw several punches.
Police say the worker was punched multiple times in the face, but refused medical attention at the scene.
Investigators say the suspect, who was wearing a mask, fled toward Williamsbridge Road.
"It's an ongoing situation, and something should be done about it," Foodtown supervisor Louis Porcelli said. "We catch people almost every day."
The attack came a day after bodega owners held a rally in the Bronx to call on state lawmakers to take action to tackle violent crime.
New York State Assemblyman Jeffrey Dinowitz is sponsoring a bill that would target repeat shoplifters.
"I'll call them the regulars, the professionals if you will, the people who do this a lot. So if you're convicted a second time within two years you will face a more significant penalty than simply petit larceny," Dinowitz said.
Dinowitz says it would do that by making the second conviction automatically a 4th degree grand larceny, which is a felony, so those "regulars" don't feel like they can keep getting away with it.
But he says that's not to be confused with those arrested not being held on bail for non-violent offenses.
MORE: Bronx small-business owners demand action on violent crime
Bronx small-business owners demand action on violent crime
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