Zuma received the Newsmaker of the Year award under Patrick Hlala in 2009.
"We are saddened by his untimely loss," Zuma said in a statement on Monday.
"On behalf of government and the people of South Africa, we wish to convey our heartfelt condolences to the family, friends, and the media fraternity."
Hlahla died at his Atteridgeville home on Sunday morning.
National Press Club chairperson Jos Charle said in a statement that Hlahla (58) died after collapsing, after he told his family he felt unwell.
"It is with great shock and disbelief that we learnt about the untimely death of our most reliable and forever smiling friend and colleague, Patrick Hlahla."
He described Hlahla as a consummate, award-winning journalist, whose mentoring had helped up-and-coming reporters become respected professional journalists.
Hlahla previously worked as a senior reporter at the Pretoria News, where he covered the metro beat for more than a decade.
Gauteng Premier Nomvula Mokonyane said Hlahla's death was a blow to journalism in the country.
"On behalf of the Gauteng provincial government, let me pass our heartfelt condolences to the Hlahla family, friends, and the entire news fraternity," she said in a statement.
"We would like to urge them to remain strong during this difficult time." – Sapa