Meanwhile, the suspect or suspects are continuing their gunfire. Two minutes later, more gunfire was heard.
Several SWAT officers on the scene were seen barricading behind cars as several gunshots went off in the neighborhood, video shows.
The two gunmen arrived in the area in a U-Haul van, each carrying long guns into the bodega, police said in radio transmissions.
UPDATE: Another round of gunfire was heard at 1:16 p.m.
A gunman is said to have fired a weapon while in Bay View Cemetery, and the officer was wounded, WABC-TV reported, before fleeing to the store on Martin Luther King Drive.
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North Jersey buses are operating on a detour in Jersey City, the agency tweeted.
One of the officers suffered potentially fatal injuries, they said.
"Our thoughts and prayers are with the men and women of the Jersey City Police Department, especially with the officers shot during this standoff, and with the residents and schoolchildren now under lockdown", New Jersey Governor Phil Murphy said.
Law enforcement sources tell PIX11 an officer was injured during the incident.
New Jersey Governor Phil Murphy wrote on Twitter, "I have been briefed on the unfolding situation in jersey City. our thoughts and prayers are with the men and women of the Jersey City Police Department, especially with the officers shot during this standoff, and with the residents and school children now under lockdown".