"Despite our best efforts, we have been unable to track the leopard down. We have launched a massive hunt for the beast," said additional district magistrate S.K. Dubey.
The cat was found inside an empty ward of an army hospital on Sunday before wildlife officers were called and managed to fire a tranquiliser dart into it, Dubey told AFP.
"But despite that he managed to break (out through) the iron grilles and escaped. He then sneaked into the premises of a cinema hall before entering an apartment block. After that we lost track of the cat," he said.
Authorities have urged the closure of markets in the city of 3.5 million until the animal, which has left six people injured, was captured, according to the Press Trust of India (PTI) news agency.
Police, soldiers and wildlife officials were trying to hunt it down but their efforts were being hampered by large crowds keen to catch a glimpse of the cat, PTI said.
Photos showed the beast pushing its way through a lattice wall at the hospital as a policeman in riot helmet, stood ready to hit it with a baton.
The leopard was also pictured leaping off a building site as people scrambled out of the way.
Last week another leopard killed a five-year-old boy in the central state of Chhattisgarh, the latest in a string of incidents raising concerns about depleting habitats for big cats which is forcing them into populated areas.
Video footage from Mumbai last year showed a leopard creeping into an apartment block foyer and snatching a small dog.
A tiger on the prowl in the northern state of Uttar Pradesh since last December is believed to have killed some ten people, and wildlife officials are still trying to hunt it down.
Conservation group WWF called for better management of forests and other habitats for India's leopard population, which numbered 1,150 at a 2011 census.
"Leopards are large territorial mammals, they need space to move around. Some of their corridors are getting blocked so there is bound to be an interface," Deepankar Ghosh of WWF-India told AFP.
"We can't put all the leopards into cages. We can't remove all the people living near forested areas. We have to manage the situation the best way we can."