A bench of justices B S Chauhan and Dipak Misra, however, said there is no urgency in taking up the matter during vacation and posted the case for hearing in July.
Sharma was today sworn in as CAG by President Pranab Mukherjee.
The 61-year-old 1976-batch Bihar cadre IAS officer replaced Vinod Rai, who demitted office yesterday after a five-and-a-half year eventful tenure.
Challenging the appointment, advocate M L Sharma, who filed the PIL, said Sharma had in the last 10 years held several sensitive positions in the defence ministry that dealt with significant procurements and appointing him as CAG would mean a conflict of interest.
"Government action is mala fide, arbitrary and under concocted scheme to justify their financial manipulation and scheme which are pending before the CAG for auditing. Impugned appointment is liable to be scrutinised by this court in the interest of justice," the petition said.