The officer says in a petition that the IAF’s decision to deny her permanent commission or full service is “biased, discriminatory, arbitrary and unreasonable”.
The Air Force has reportedly been asked to respond in four weeks.
Wing Commander Thakur was the first woman officer to lead the Inter-Service Guard of Honour inspected by President Obama in 2015.
The daughter of an army colonel, the Rajasthan officer joined the Air Force in 2000.
The Air Force recently allowed women fighter pilots for short service commission.