The plea, filed by Shah, termed the army chief's extension as "illegal and invalid''.
Bajwa was appointed by erstwhile Prime Minister Nawaz Sharif in November 2016.
Fifty-eight-year-old Bajwa previously served as the Commander of Rawalpindi Corps. He was also employed as the Inspector General, Training and Evaluation, at GHQ, a position earlier held by his predecessor Raheel Sharif.
As a brigadier, he served as the Chief of Staff at X Corps and commanded formation division in Northern Areas as the Formation Commander (FCNA).