The incident occurred at Dhorwada in Dharavi when Mahakrishna Nadar (25) was climbing stairs to deliver the cylinder, police said.
According to Dharavi Police, the cylinder slipped from Nadar's shoulders and landed on the head of Mohammad Bilal Sheikh who was sleeping in that lane.
Sheikh was rushed to civic-run hospital, where he was declared dead before admission, an official said.
Nadar has been booked under section 304-A (causing death by negligence) of IPC, and arrested him subsequently, the official said.