Tynes, who kicked the winning field goal in overtime of the NFC title game against Green Bay last year, injured his knee in training camp and had arthroscopic surgery before the season.
Veteran John Carney was signed days before the season opener. He has hit all nine of his field goal attempts and all eight extra points in helping the Giants win their first three games.
Tynes has been practicing in recent weeks and seemingly was making progress.
However, he said after Wednesday's workout that he is having problems.
"The important thing is for me to be healthy and get back to 100 percent, which I am not at," he said. "I keep thinking I am, but after each workout I keep having swelling in my knee. I am going to go in and treat it because it is swelling right now. It's just a matter of time before I get it under control."
Tynes said that the medical staff told him this would be a six- to eight-week injury. He has been out six weeks now.
"As a player I wanted to come back faster than I should," Tynes said. "The bonus is John is kicking well and we don't have any roster problems. Most teams have three specialists and we have three specialists. We are not hurting for me to come back."
Coach Tom Coughlin has no plans to make a decision on a kicker right now, and he added on Wednesday that the possibility existed that he would not have to make a decision between Tynes and Carney.