The two approached one another near midfield after the game and exchanged blows before being separated by teammates.
Ramsey is the father of two of Tate's nieces and the two have shared bad blood since Ramsey reportedly ended a long-term relationship with Tate's sister during her pregnancy last year. Both players hail from Nashville.
Neither Ramsey nor Tate were made available to the media after the game. The league is set to review the scuffle, but as of now, no suspensions are anticipated, but fines could be coming, NFL Network's Tom Pelissero reported.
They shared one memorable sequence within the Rams' win, with the Pro Bowl corner slamming Tate to the ground after a short completion. Ramsey had five tackles, including one for a loss, to help lead a stellar defensive effort as the Giants were held to just three field goals. Tate recorded four catches for 20 yards.
Following the skirmish, Ramsey remained on the field for an extended period of time while on the phone and speaking to Rams personnel.
"We don't want to have happen at the end of the game what happened," Giants coach Joe Judge said afterward, per NJ.com. "That's not the way we want to be as a team."