Jahangir Alam Khan Moon, 65, was at the club in the central city of Multan, 420 kilometres (263 miles) from Islamabad when university students gathered outside, chanting slogans and blocking the road, his cousin Mohsin Raza said.
Students from the Veterinary Science department of the Bahauddin Zakariya University were demanding that the government recognise their degrees.
Pakistani protesters routinely gather outside press clubs in a bid to maximise media coverage of their demands.
"A motorcycle carrying a patient arrived and some journalists went to convince the students to let it pass," Raza told AFP. "A scuffle broke out and the students started pelting stones and several journalists were wounded."
Moon, a freelance sports correspondent, was one of those hurt.
"He was hit in the head by a stone. He went to hospital and received some stitches. When he returned home he went to his room to change his clothes but he died," said Raza, who is himself a journalist.
"It was not clear why he died. It could have been a heart attack."
Police said 39 people were detained on charges of resorting to violence. Local police chief Amir Zulfiqar promised action against the culprits.
The death comes just two weeks after Pakistani journalist Saleem Shahzad was found dead on May 31 outside the capital in a killing blamed on his coverage of links between rogue navy officials and al Qaeda.
At the time, Reporters Without Borders said 16 journalists had been killed since the start of 2010 in Pakistan, which it ranks 151st out of 178 countries in its press freedom index.
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