The spokesman added that India lost one MiG-21 aircraft today and the pilot is missing in action.
Raveesh Kumar said yesterday's air strikes was based on "credible inputs".
"Pakistan has responded this morning by using its Air Force to target military installations on the Indian side. Due to our high state of readiness and alertness, Pakistan's attempts were foiled successfully," Kumar said.
He said PAF was detected and the Indian Air Force responded instantly.
"In that aerial engagement, one Pakistan Air Force fighter aircraft was shot down by a MiG 21 Bison of the Indian Air Force. The Pakistani aircraft was seen by ground forces falling from the sky on the Pakistan side."
"In this engagement, we have unfortunately lost one MiG 21. The pilot is missing in action. Pakistan has claimed that he is in their custody. We are ascertaining the facts," he said.
ANI news agency had earlier reported that India had shot down Pakistan Air Force's F-16 fighter jet in Jammu and Kashmir's Nowshera sector.
The fighter jet was one of the three planes which violated Indian airspace and reached Nowshera on Tuesday morning. As tensions escalated, Indian authorities closed airports in Leh, Jammu, Srinagar and Amritsar for civilian traffic. The Pathankot airport was put high alert.
Meanwhile, US Secretary of State Mike Pompeo urged India and Pakistan to exercise restraint and avoid escalation at any cost.
On Monday, India's Mirage 2000 fighter jets carried out air strikes across the Line of Control(LoC) in Balakot in retaliation against the terror attack on CRPF personnel on February 14th.
Raveesh Kumar said yesterday's air strikes was based on "credible inputs"