The incident unfolded Thursday at 610 Exterior Street while the victims were waiting in line at BJ's Wholesale Club.
Police say the male and female suspects got into an argument with the three victims after someone may have cut the line.
The female suspect pulled out a sharp object, possibly a boxcutter, and sliced a 38-year-old woman and her 15-year-old daughter in the face.
Authorities say the suspect then stabbed another 38-year-old customer, unknown to the mother and daughter, in the arm.
The mother and daughter were taken to an area hospital and were said to be stable.
The other customer refused medical attention.
Police say the male suspect tried to assault the victims during the fight.
Both the male and female suspects were arrested and taken into custody.
MORE NEWS: 30 NYC businesses requiring proof of COVID vaccination
* More Bronx news
* Send us a news tip
* Download the abc7NY app for breaking news alerts
* Follow us on YouTube
Submit a News Tip