The New York Post quoted Mara as saying that Beckham faced internal discipline from the Giants following the incident, which was penalised during the game.
"I do not want to get into a discussion about this, but I will say that I am very unhappy with Odell's behavior on Sunday and we intend to deal with it internally," Mara was quoted as saying.
Beckham, one of the biggest stars in the National Football League, earned his team a 15-yard penalty after he celebrated an end zone catch by dropping to all fours and cocking his leg like a dog.
Beckham later said on Twitter his gesture was a political statement directed at President Donald Trump following the US leader's criticism of NFL players last week.
However immediately after the game, Beckham did not mention Trump and took issue with the penalty.
"I was in the end zone. I scored a touchdown," Beckham said. "I'm a dog so I acted like a dog. I don't know if the rulebook said you can't hike your leg. (The referee) said I peed on somebody, so I was trying to find the imaginary ghost that I peed on. But I didn't see him."
The NFL has relaxed rules on touchdown celebrations this season after a string of penalties last year which saw the organisation dubbed the "No Fun League." However celebrations which relate to a "bodily function" continue to be forbidden.