Answer by Raakhee V. Menon:
Although there is no direct reference to ‘Mumbai’ as such in the Mahabharata, the area currently called Mumbai was a part of the Konkana region which was a part of Shurparaka, a kingdom founded by Lord Parashurama, close to the mouth of the Narmada river. It lay very close to the Kingdom of Vidarbha, maternal home of Queen Rukmini, Lord Krishna’s chief Queen. Shurparaka finds a definite mention in the Mahabharata. Parashurama gave this kingdom to the Brahmin rulers of Kashyapa clan. Shurparaka is identified with medieval Sopara and modern day Nala Sopara, very close to the current city of Mumbai. The Shurparaka kingdom was annexed by the Pandava prince Sahadeva at the time of the A̶s̶h̶w̶a̶m̶e̶d̶h̶a̶ ̶Y̶a̶g̶n̶a̶ ̶o̶f̶ ̶Y̶u̶d̶h̶i̶s̶h̶t̶h̶i̶r̶a̶ ̶a̶f̶t̶e̶r̶ ̶t̶h̶e̶ ̶K̶u̶r̶u̶k̶s̶h̶e̶t̶r̶a̶ ̶w̶a̶r̶ Rajasuya Yagna of Yudhishthira before the Kurukshetra war.
The coastal islands were predominantly inhabited by Koli fishermen. It was much later that the area was conferred onto a family of vassals of the then Rashtrakuta king, Govinda II. This feudal clan was known as the Shilahara Dynasty and occupied most of the areas of present day Mumbai, Thane, Raigad, etc.