Rodriguez was arrested and charged with third-degree assault after Wednesday night's game. The team put him on the restricted list and removed him from the active roster.
The Mets said he will not be with the team during that time. If the ban is not reversed, Rodriguez would lose $125,683 of his $11.5 million salary.
"Ownership and the organization are very disappointed in Francisco's inappropriate behavior and we take this matter very seriously," Mets chief operating officer Jeff Wilpon said.
The 28-year-old closer went into the family lounge, hauled his father-in-law into an adjoining tunnel and "repeatedly hit him in the face and hit his head against a wall" before taking off, NYPD spokesman Paul Browne said.
A Mets official called police while a clubhouse employee was instructed to call Rodriguez on his cell phone. Rodriguez came back about 15 minutes later and was taken into custody. Browne described Rodriguez as cooperative with officers when he returned. Rodriguez was arrested and held at the ballpark after the 6-2 loss to Colorado.
His father-in-law - identified by authorities as 53-year-old Carlos Pena - was in a hospital with a scraped face and bump on his head. Pena had swelling above his right eyebrow.
An hour before Thursday's game against Colorado, no court action had been taken. Before the suspension was announced, Rodriguez's lawyer, Jay Reisinger, declined comment in an e-mail to The Associated Press.
Mets manager Jerry Manuel, speaking before the suspension, had said he wouldn't hesitate to use Rodriguez during Thursday's game if the pitcher was available.
General manager Omar Minaya, at the owners' quarterly meetings in Minneapolis, had declined to comment before the suspension was put in place.
Right-hander Ryota Igarashi was recalled from Triple-A Buffalo to fill Rodriguez's roster spot and the Mets expected him to arrive during Thursday's game.
Manuel said Rodriguez's actions were not a distraction to his slumping team, who began the day fourth in the NL East at 56-57. "We've had a lot of things go on here and there," he said. "We are men and things come our way and we still have a job to do. We have to perform, which right now we're not doing very well at, but we still have to put forth our best effort."
Several security guards, along with some women and children, were seen around the Mets' family lounge. The room is near the clubhouse and ordinarily a convivial spot where players meet their relatives after games.
Mets shortstop Jose Reyes said his wife and daughter were in the family room when it happened.
"I don't know exactly what happened," Reyes said. "You don't want to see that happen, especially here at the ballpark. I hope he comes clean about what happened because we need him here." Mets outfielder Jeff Francoeur's wife was in the lounge. "I think it happened more outside, I think, not directly in the family room," he said.
Rodriguez has had previous confrontations with a team official, a coach and an opponent in his 1½ seasons with the Mets, though none reached this level.
"Maybe it's a distraction we need," Francoeur said. "Not to say it's a good thing. But maybe at the end of the day we can turn it into a positive. I know for him, it's between him and his family."
The excitable pitcher signed a $37 million, three-year contract with the Mets after saving a record 62 games with the Angels in 2008. He is 4-2 with 25 saves and a 2.24 ERA this season.
The loss Wednesday night dropped the Mets below .500. Reliever Manny Acosta gave up a two-out grand slam to Melvin Mora in the eighth inning.
In May, Rodriguez and bullpen coach Randy Niemann got into a heated exchange while the pitcher was preparing to enter a game. Manuel later said the matter was resolved, without divulging what caused the dispute.
In July 2009, Rodriguez and former Mets official Tony Bernazard argued aboard the team bus. Bernazard was later fired by the Mets amid several allegations.
That June, Rodriguez and New York Yankees reliever Brian Bruney needed to be separated before a game. They had jawed at each other in the media a day earlier.
AP Baseball Writers Ben Walker in New York and Jon Krawczynski in Minneapolis and Associated Press Writer Tom Hays in New York contributed to this report.