Brinson is accused of stabbing 41-year-old Mohinder Singh during an attempted robbery at the deli on Nov. 30.
Union County Prosecutor Theodore Romankow said a knife believed to be the murder weapon was found nearby.
Singh, who lived in an apartment nearby, was found dead inside the store by a customer. Police say the assailant was injured during the attack and left a trail of blood leading out the deli's back door.
An arrest warrant for the suspect was issued Sunday and bail was set at $750,000.