As per aviation regulator DGCA norms, airlines close the check-in counters for all domestic fights 45 minutes prior to departure.
Reddy, who represents Andhra Pradesh's Anantapur seat in the Lok Sabha, reported late for the flight and therefore, was not allowed to board it, a source said.
He was scheduled to fly IndiGo's flight 6E-608, which departs from the Viskahpatnam airport at 8.10 am, to Hyderabad.
"On being informed by the airline staff that he was late and cannot be issued a boarding pass, an enraged Reddy went to the IndiGo office next to the check-in counter and created a ruckus," the airline source said.
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"We are investigating the matter and have no further comments to offer," the Gurgaon-based airline said in a statement.
"The safety and security of our colleagues and customers is our highest priority," it said.
Reddy was not available for comments.
He had last year allegedly damaged furniture at Air India office at Gannavaram Airport in Vijayawada after missing his flight for similar reasons.
Union Civil Aviation Minister Ashok Gajapathi Raju also belongs to the TDP.
Earlier this year, Shiv Sena MP Ravindra Gaikwad was temporarily banned by airlines from flying after he assaulted an Air India staffer.
The government is likely to release the no-fly list rules by June 20.
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