Sadpara was the first Pakistani to scale all five of the country's "eight-thousanders" which tower above 8,000 metres - among the 14 highest mountains on the planet.
That included K2, the world's second highest mountain but considered a more challenging climb than the highest, Mount Everest, in Nepal - which Sadpara had also climbed.
Sharif spoke of the country's pride in Sadpara, who leaves three sons and a daughter, as social media was flooded with tributes.
"The man for whom no mountain was high enough! #RIP #Hassan Sadpara, legendary mountaineer!" tweeted Faran Rafi, just one of many such messages.
Sadpara's son Arif told AFP his father died around noon in the garrison city of Rawalpindi next to the capital Islamabad.
Sadpara, who was born Hassan Asad, came from a small village near the town of Skardu in the mountainous Gilgit-Baltistan region in Pakistan's north.
But his fame did not bring him fortune, with his family urging the government to help finance his cancer treatment as they began to run out of money.
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