It will come into effect after Municipal Commissioner Ajoy Mehta gives his administrative nod.
BJP corporator Sandeep Patel tabled a notice of motion, which was supported by the ruling Shiv Sena, and Mayor Vishwanath Mahadeshwar approved it.
The Congress and Samajwadi Party (SP) corporators boycotted the proceedings, alleging that they were not allowed to put forth their views.
"A recent Madras High Court ruling, which made singing of 'Vande Mataram' mandatory in the schools of Tamil Nadu, gave me the idea that if it can be done there, then why not in Mumbai," Mr Patel told PTI.
"So, I tabled the motion and I am grateful that the mayor approved it after finding enough support for it," said the first-time corporator from the Goregaon area.
"We need to instill a sense of patriotism in our youth as they should remember the glorious period of our freedom struggle," the BJP member said.
However, the group leader of main opposition Congress, Ravi Raja, alleged that the BJP and the ruling Shiv Sena were "trying to impose" their will on everyone.
"We don't oppose singing of Vande Mataram in schools, but the way it is going to be imposed, we object to that. This would violate our fundamental rights as enshrined in the Constitution and therefore, I am going to write a letter to the municipal commissioner," he said.
SP's group leader in the House Rais Shaikh said the move was "unacceptable".
"Let me clarify that we are not opposing Vande Mataram. Whenever and wherever it is sung, we give it due respect. What we are opposing is it being made mandatory. Since we were not allowed to put forth our view in the House, we will meet the commissioner and put across our point," he added.
The Madras High Court ruling had triggered a political slugfest in the Maharashtra Legislature, with a BJP MLA demanding its implementation in schools and colleges of the state, while the All India Majlis-e-Ittehadul Muslimeen (AIMIM) and SP MLAs opposed the proposal.