Souder said in a statement provided by his office that he has "sinned against God, my wife and my family by having a mutual relationship with a part-time member of my staff."
He scheduled a news conference in Fort Wayne on Tuesday to discuss his decision.
Souder won a bruising Republican primary on May 4 to be nominated for his ninth term representing northeastern Indiana.
Souder, 59, said he also would not be a candidate in the fall election.
"I believe it is the best decision for my family, the people of northeast Indiana and our country," he said in the statement.
"In the poisonous environment of Washington, D.C., any personal failing is seized upon, often twisted, for political gain," he said. "I am resigning rather than to put my family through that painful, drawn-out process."
Souder won the Republican primary over car dealer Bob Thomas, who spent much of his own money on television commercials portraying Souder as a career politician who wasn't a true fiscal conservative. Souder countered by emphasizing his A-plus marks from the National Rifle Association and 100 percent rating from the National Right to Life Committee.
Souder had been expected to face a stiff challege from Democrat Tom Hayhurst, a former Fort Wayne city councilman who lost a close race to Souder in 2006.
Souder did not provide details about the affair.
"As I leave public office, my plans are focused upon repairing my marriage, earning back the trust of my family and my community, and renewing my walk with my Lord," he said.
