In an e-mail to supporters, Rogers said he had "determined that the best way for me to continue to have a direct impact for my constituents and the nation is to remain in the House of Representatives," the Washington Post reported.
The decision was not unexpected. His brother said in a recent interview he didn't expect the congressman to run for the seat and the National Republican Senatorial Committee had not met with him.
Rogers is chair of the House Intelligence Committee, a position he would have lost as a senator.
By bowing out of the senatorial race, Rogers leaves former secretary of state Terri Lynn Land as the only GOP candidate. Rep. Justin Amash is considering getting into the race.
Rep. Gary Peters is expected to take the Democratic nomination.