The Giants said Moore was "suspended by the team pending further investigation."
NJ Advance Media, citing the criminal complaint and affidavit, reported that Moore was charged with third-degree aggravated assault after allegedly punching a woman, knocking her unconscious and stepping on her neck on Thursday at his home in Linden, New Jersey.
The woman had visible injuries to her neck and face when she was examined at a hospital.
The 22-year-old woman, who has been dating Moore since January, according to the affidavit, filed her complaint on Saturday. Police were not called to Moore's home on Thursday, NJ Advance Media reported.
According to the report, the woman went to Moore's home on Thursday after he didn't respond to text messages. When she arrived, she was confronted by another woman and the two began fighting. Moore is accused of watching the confrontation and then stepping on her neck after she fell to the ground. He then allegedly punched her when she returned to her feet.
MBK Sports, which represents Moore, has retained attorneys Alex Spiro and James Abate to handle Moore's defense against the charge.
"We remain confident that when the truth is revealed, Mr. Moore will be exonerated and vindicated completely of these baseless charges," MBK Sports president and agent Eugene Lee said in a statement.
"The claimant in this matter showed up unannounced and unsolicited at Mr. Moore's home to begin an altercation with Mr. Moore's girlfriend and invent these accusations. He will be fully cleared of all charges," Spiro said in a statement.
Moore, 22, signed with the Giants as an undrafted free agent last year and appeared in two games.