Granting the stay, a bench comprising Chief Justice M Y Eqbal and Justice T S Sivagnanam issued notice to the government and directed it to file a counter affidavit in six weeks.
The petition was filed by advocate P Pugalenthi, who claimed the November 1 decision of the state cabinet to shift the library would be "arbitrary, unfair and unreasonable."
The petitioner contended that moving the library out of the building, constructed with public money, was also violative of the Constitution and the decision deserved to be declared as arbitrary and mala fide.
Abandoning another of her arch rival DMK chief M Karunanidhi's pet projects, Chief Minister Jayalalithaa had announced on Wednesday that the Library, claimed to be Asia's largest, will be converted into a super-speciality paediatric hospital.
Since her return to power with a landslide victory in the April 13 elections, this is one of the major DMK initiatives overturned by Jayalalithaa after announcing her government's decision to convert the new Assembly-Secretariat complex into a super-speciality hospital.
Justifying her decision on shifting the library to the DPI complex at Egmore, she had said such a super speciality paediatric hospital has not been established anywhere in India so far.
Various political parties and book lovers had come out strongly against the government's move.
The library was constructed at Kotturpuram near the Anna University, a site chosen by the AIADMK government during 2001-06 for the construction of a new secretariat complex