The former House Majority Leader had sustained stress fractures in both his feet during rehearsals and performances for the ABC show.
He had been partnered with professional dancer Cheryl Burke.
During last night's results show, he said: "I won't [continue to dance]. You can't practice and if you can't practice you would make a fool of yourself out here.
"I don't want to do that to Cheryl because she's so great."
DeLay had been advised by producers and doctors not to perform on Monday night's show but went ahead with his samba routine anyway. Despite scoring just 15 points from the judges, the public had voted him through to next week before his retirement.
"Those voters keeping me safe against Len Goodman's scores - that was just fantastic," he said.
His next dance would have been the Texas two-step and he accepted an offer from host Tom Bergeron to perform the routine on the season finale if he had recovered.