The two contract workers were removing blocks in the drainage when the incident occurred, police said.
Coming down hard on civic bodies continuing with the practise of manual scavenging, which has reportedly led to a number of deaths since 1993, the Madras High Court had last month directed it to follow the law prohibiting this type of work, as also various directions of the court in this regard.
The court had directed the Corporation to comply with the Prohibition of Employment as Manual Scavengers and Their Rehabilitation Act-2013 and its directions on the matter.
City Corporation Commissioner Kathivaran said that an inquiry had been ordered into the incident. Compensation would be provided to the families of the two, he said.