Police and paramilitary rangers deployed tear gas and water cannon on the protesters after they blocked the main entrance to Karachi's Jinnah International Airport around midday.
A spokesman at the Agha Khan hospital said one of the protesters, identified as Inayat Raza, had died of a gunshot wound. "The PIA employee was brought dead at our emergency department and our team attempted to revive him for 20 minutes," the spokesman said.
Nadeem Jaffer, a colleague and friend of Raza, confirmed his death at the hospital.
Seemi Jamali, head of the emergency department at the city's main Jinnah Post Graduate Medical Centre said the hospital had received four injured people, including two with non-fatal gunshot wounds.
Both law enforcement agencies denied they had opened fire on protesters.
Kamran Fazal, the police chief of the city's eastern district said: "The situation escalated when a couple of gunshots were fired. My officers told me that they might be fired from the crowd.
"We are searching for the empty shells and only then can we establish who opened fire."
The PIA employees' union had announced a day earlier its plans to shut down the airline's flights after weeks of token strikes against government proposals to complete the partial sale of the carrier by July.
The move follows years of crushing losses and mismanagement that have battered the airline's reputation.
PIA, one of the world's leading airlines until the 1970s, now suffers from frequent cancellations and delays and has been involved in numerous controversies over the years, including the jailing of a drunk pilot in Britain in 2013.
