The court issued a notice to all parties including the Pakistan defence ministry and General Bajwa.
General Bajwa was due to retire on November 29, however, he was given an extension for a period of three year by Pakistan PM Imran Khan on August 19.
Pakistan's Supreme Court said that the cabinet has 25 members but only 11 members voted in favour of the resolution, therefore the extension was given without the consent of the majority of the cabinet.
The court further said that only the president of Pakistan can approve the extension of tenure for the Army chief.
The hearing in the case has been adjourned till Wednesday.
Bajwa has held the post since November 29, 2016, and was appointed by former Prime Minister Nawaz Sharif.
Prior to his appointment, Pakistan's Army chief had served as the Inspector General of the Training and Evaluation at the Army General headquarter. He had also served as field commander of X Corps from August 2013 to September 2015.
In 2007, General Bajwa had served as a Brigadier in the United Nations mission in Congo and as a brigade commander.
Pakistan's Supreme Court said that only the president of Pakistan can approve the extension of tenure for the Army chief.