The injury occurred when he got his leg tangled with cornerback Janoris Jenkins on a deep pass down the left sideline.
Beckham attempted to return to practice before limping off the field.
"He got cleated and has a cut or two. They're taking a look now," coach Ben McAdoo said after practice. "So he's probably going to be sore here for a couple days."
The Giants are off Monday before their first fully padded practice of the summer on Tuesday.
Beckham limped to his post-practice news conference and said he bled a bit from Saturday's incident, but it blended in with his custom "Dexter" cleats, he said with a smile.
The injury isn't anything that has Beckham or the Giants concerned long term.
"After I went down it was kind of, 'You're done for the day,'" Beckham said. "There are plenty of more days for camp. It will be all right.
"Minor setback for the time being."
That's a relief for the Giants. Beckham was their leader last season in catches (96), receiving yards (1,450) and touchdowns (13). The Giants are finally hoping to have Beckham and Victor Cruz on the field together this year. Cruz has missed 26 straight games and has played with Beckham for parts of two games over the past two seasons.
The Giants have put extra emphasis on remaining healthy this summer. On Sunday, Beckham was the first player to leave any of their three practices with an injury.
"When something happens to any of your players your heart is in your throat," McAdoo said. "But we were fortunate there."