The Giants announced Tuesday that the 12-year veteran was seen by orthopedic surgeon Russell Warren and vascular surgeon John Karwowaki on Monday at the Hospital for Special Surgery in New York.
Rogers experienced swelling in his lower leg after playing in the preseason opener Friday. He missed practice Sunday and Monday.
The Super Bowl champions did not say how long he would be sidelined, but New Jersey Devils defenseman Henrik Tallinder missed a couple of months this past NHL season after developing a blood clot in his leg.
The Giants also said defensive tackle Martin Parker has a herniated disc in his back that will require surgery, and that fellow defensive tackle Marvin Austin is being seen by doctors in New York for a back problem.
Parker was hurt in Friday's game. Austin practiced Monday.
Defensive end Justin Trattou, who has been sidelined since early in training camp at the University at Albany with ankle and heel injuries, was examined by ankle specialist Dr. David Levine and is not expected back on the field for a couple of weeks.
UPDATE: Giants coach Tom Coughlin has said that Rogers' injury is season ending and that it is "very sad," according to Ebenezer Samuel of the New York Daily News.
The Associated Press contributed to this report.