Reddy, who was in Kullu for a meeting of a Parliamentary Standing Committee, suffered cardiac arrest at Bhuntar airport, a senior government functionary told IANS.
Other accompanying MPs rushed him to the Regional Hospital in Kullu, where he died while undergoing treatment.
Kullu town is some 200 km from Shimla.
The parliamentary delegation, comprising their families, reached Bhuntar, located on the outskirts of Kullu, by a plane in the morning from New Delhi, an official said.
Telangana Chief Minister K. Chandrasekhar Rao condoled the death of the senior leader. He spoke to K. Prabhakar Reddy, the MP from Medak, who was with Govardhan Reddy for the parliamentary panel meeting.
Rao directed Chief Secretary S.P. Singh and Resident Commissioner of Telangana in Delhi Aravind Kumar to make arrangements for bringing Reddy’s body to Hyderabad by a special aircraft.
Born in Nalgonda district on November 20, 1936, Reddy was a loyal Congress leader and was close to the Nehru-Gandhi family.
He was elected to the legislative assembly of Andhra Pradesh five times, before Telangana was formed. He also served as a cabinet minister in the cabinets of Bhavanam Venkatram and Vijayabhaskar Reddy.
Reddy began his political career as a leader of the National Students Union of India (NSUI) in Osmania University in the 1950s. He was General Secretary of the Andhra Pradesh Youth Congress during 1962-64.
He was first elected to the state assembly from Munugode constituency in Nalgonda district in 1967.
He was elected to the Rajya Sabha in 2012.
Reddy was representing Telangana in the Rajya Sabha since 2014 and served as a state minister twice during the 1980s.