Education Minister Sikander Singh Maluka had asked Principal Secretary (Education) S S Channi to probe the whole matter, officials said.
Maluka also asked him to submit the report within the stipulated time to fix accountability for wrongdoings, if any, they said.
The inquiry was ordered after a media report alleged a large number of ineligible teachers were promoted as lecturers by the education department.
The minister said he was determined to provide a clean and transparent administration and any employee found involved in any unfair practice would not be spared.