Senator Dodd, 65, speaking at a news conference in Hartford said "I feel fine; I'm going to be fine. We caught this early."
Dodd is chairman of the Senate Banking Committee and also is playing a lead role in Congress' overhaul of the nation's health care system.
He took that role while his close friend, Senate health committee Chairman Edward Kennedy, D-Mass., battles brain cancer.
In an earlier statement, Dodd said, "After a week or two of recuperation, I expect to be right back to work."
Dodd is facing a tough bid for re-election in 2010, but his surgery and recovery are not seen as affecting his re-election campaign.