The 22-year-old Baig, from the small town of Shimshal in the Hunza valley in Pakistan's mountainous north, scaled the 8,848 metre peak early yesterday after a gruelling expedition in rough weather.
Karrar Haidri, member executive council of Pakistan Alpine Club (PAC), said Baig had raised Pakistan's name in the world.
"She is a brave girl who summited the peak and sent us a message of her achievement and the whole Pakistan is feeling proud of her," Haidri told AFP.
"She used her own resources and despite rough weather and fears of avalanche she never lost courage."
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Baig was among 146 climbers to reach the world's highest peak yesterday, including the first woman from Saudi Arabia, Indian sisters who were the first twins, and a British climber who gave a live video interview via his smartphone.
British mountaineer Daniel Hughes was interviewed by the BBC in what he called the first live video call from the summit, but Nepalese officials told AFP he had broken the law by not seeking official permission to broadcast.
In 2010 Baig became the first person to scale the 6,000-metre Chashkin Sar peak in northern Pakistan and the mountain is now named "Samina Peak" in her honour.
"I sincerely hope that Samina's achievement will induce more and more woman to join this sport and help us convince the government to give more funds to us so that our people can attain more height in this department," said Haidir.