Carnahan filed to run Tuesday morning to fill the seat now occupied by Clay, who filed for re-election less than an hour later, the St. Louis Post-Dispatch reported.
The two are vying for the 1st District seat, which includes all of St. Louis.
Carnahan said Tuesday he hopes a legal challenge will lead to the new map being declared unconstitutional.
But, Carnahan said, "I made it clear over a year ago that I'm running for re-election regardless of how the maps turn out."
Clay, facing his first tough opponent in more than a decade, said he would prevail and noted the new 1st District includes only 20 percent of Carnahan's old district.
"He doesn't have a chance," Clay said. "Eighty percent of the district is the district I've represented for 12 years. I'm very confident. I look forward to presenting my record as a strong committed progressive."
Clay took over the seat from his father, Bill Clay, in 2001.
Carnahan's father, Mel Carnahan, had been governor, and his sister, Robin Carnahan, is secretary of state.