Placing Burress on the non-football injury list also will keep him out of the playoffs. The Giants (11-2) won the NFC East title on Sunday.
Union spokesman Carl Francis said the grievance will be heard by an arbitrator after the season ends.
Under the contract that Burress signed in September, the Giants owe the Super Bowl star $1 million of his signing bonus on Wednesday. Team spokesman Pat Hanlon had no comment on either the grievance and whether the team would pay the signing bonus.
Francis said the union would consider another grievance if the Giants withheld the payment.
Agent Drew Rosenhaus did not return either an e-mail or a telephone call left by The Associated Press seeking comment.
The union filed another grievance on Burress' behalf earlier this year after the Giants suspended him for a game and fined him two weeks pay for missing a team meeting in September.
The two sides eventually agreed to cut the fine in half, saving Burress about one game's pay - more than $200,000.
The latest action against Burress was last Tuesday, just a day after the 31-year-old was booked and arraigned on charges of criminal possession of a weapon relating to the shooting in New York on Nov. 29.
He pleaded not guilty, posted $100,000 bail and left.
The shooting was the latest run-in that Burress has had with the team since signing as a free agent in 2005. He has admitted to being fined dozens of times for violating team rules. In addition to his suspension in September, he also was fined $45,000 by the league for abusing an official and throwing a ball into the stands in a game with San Francisco on Nov. 19.
Burress has not spoken about the shooting at the Latin Quarter nightclub in Manhattan, and the focus of the investigation the past week has been on the role of Giants middle linebacker Antonio Pierce.
After making authorities wait almost a week, Pierce talked to investigators on Friday about the shooting. Neither Pierce's attorney nor the police would reveal what was said.
Authorities are interested in why neither Pierce, who drove Burress to New York-Presbyterian Hospital/Weill Cornell Medical Center, nor Dr. Josyann Abisaab, the doctor who treated the receiver, called police to report the shooting.
Abisaab has since been suspended for not reporting the gunshot injury, as required by law.
Police said that she is supposed to speak with authorities this week, but neither police and nor the district attorney's office refused to comment Tuesday when asked when the meeting would take place.
Burress was shot when he fumbled with the glass in his hand and the .40-caliber Glock that he was carrying in his pants slipped down his leg. The man who caught the go-ahead touchdown pass in the Super Bowl then reached for it and accidentally pulled the trigger and shot himself.
He faces a felony weapons possession charge that requires a mandatory minimum 3½ years in prison.
