The 34-year-old rhino was brought to the Byculla Zoo in 1985 from Assam when he was six years old.
The veterinary officers from Delhi had positioned the transport cage near Shiva's enclosure on August 13, and were waiting for the animal to enter the cage.
A press release from Municipal Corporation of Greater Mumbai said that an animal has to be shifted to another zoo if the zoo where it is lodged does not have a companion.
The Bombay High Court as well as the National Zoo Authority (NZA) had directed the civic authorities to find a female companion for Shiva in 2004.
Finally, it was decided that he should be shifted to Delhi zoo, where there are two female rhinos.
Shiva is being taken to Delhi by road, authorities said.