According to AIIMS Trauma Centre sources, the officer is currently admitted to the ICU and underwent brain surgery.
Doctors said the officer had fractures in the upper limb, head injuries and "maxillofacial" injury.
He is under constant observation, they said.
45-year-old Cheetah was flown in an air ambulance from Srinagar yesterday from the military hospital where he was initially admitted after the encounter.
Hailing from Rajasthan, Cheetah bore the initial brunt of the attack in Hajjan area where a joint team of army, CRPF and state police had laid siege following intelligence inputs that two foreign terrorists were hiding in the area.
45-year-old Cheetah commands the 45th Battalion of the Central Reserve Police Force (CRPF) deployed in the Kashmir valley.
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