Coughlin told reporters during a conference call Sunday that an MRI exam showed no major damage.
"I'm not going to predict how long he'll be out," Coughlin said. "He'll be a fulltime participant in the training room. That's for sure."
Coughlin was not sure whether the Giants would sign a kicker this week but it seems unlikely that Tynes will be able to play a week from Monday against Chicago.
"We have one solid option if we decide not to do that, but if we decide (that) then it will be relatively early in the week, obviously," said Coughlin, who indicated he didn't want to burden punter Matt Dodge with kickoff duties because the second-year player is competing with Steve Weatherford for a job.
Tynes was on crutches after the game, the result of being run into on a blocked second-half field goal. He wasn't pleased.
"Where was the flag?" he said in Sunday's edition of the New York Post. "What happened to the defenseless player (emphasis)? I don't care if you tip the ball, you still shouldn't be able to hit a kicker when he still has his plant foot on the ground.
"I don't understand where the hell the rule is, because I was the epitome of a defenseless player," Tynes added. "I guess we'll find out soon enough. I'm sure I'm talking out of school, but whatever."
The league has put new rules in place this season in an attempt to increase player safety, but no foul was called on the play.
The Associated Press contributed to this report