"The decision was taken by the party, as he gave some personal reasons," Aam Aadmi Party spokesperson Nagendar Sharma told IANS.
He said Singh has agreed to withdraw from the contest.
Singh told IANS he had "no complaints with the party decision".
"I will still be a (party) member and campaign (for the AAP)," he said, adding that the party was free to pick the best available candidate.
Earlier, an AAP leader told IANS that the party was unaware of the cases filed against Singh, a social activist.
Rakhi Birla, a former journalist, was the youngest minister in the 49-day-long Arvind Kejriwal government in Delhi.