The hospital authorities had allegedly violated the approved building plan for the eight-storey building. The High Court had ordered the demolition to begin from June 16.
A vacation bench comprising Justices Indu Malhotra and M.R. Shah on Monday also directed Billroth Hospitals Ltd to refrain from using the top five floors of the building for any activity.
The Supreme Court issued notice and sought a reply on the issue from the Tamil Nadu government.
Billroth Hospitals had moved the apex court challenging the High Court order.
The court also granted 10 days to the hospital authorities to vacate these floors.
Counsel for the hospital, senior advocate Abhishek Manu Singhvi, submitted before the court that the authorities had applied as per the 2017 building regularisation scheme of Tamil Nadu. The court observed that the construction is without any authorised plan.
Singhvi informed the court that the 2017 scheme matter is pending, and the hospital has been operational since 2005-2006.
The court rebutted the argument that it is issuing notice only because the High Court had set aside the scheme in a contempt case.
"You have to stop using it...for 10 years, you (hospital) have done it," the bench observed while granting a stay on the High Court verdict.
Responding to Singhvi's argument on staying the High Court order, the apex court said that it will grant a stay on condition that the floors in question be put out of operation.
The matter will come up for its next hearing after the summer vacations of the Supreme Court.
( With inputs from IANS )