The 56-year-old great was admitted to Medanta - the Medicity - earlier this month after a bout of jaundice and dengue made his condition worse. He was airlifted from Varanasi.
"He breathed his last at 10:45 this morning. It was multiple organ failure that led to his passing away. He will be taken to Varanasi and last rites will be performed there tomorrow," Shahid's son Mohammed Saif told PTI.
Known for his brilliant dribbling skills, Shahid was considered one of India's greatest hockey players. He was a member of the V Baskaran-led Indian team that won a gold medal at the 1980 Moscow Olympics.
Prime Minister Narendra Modi joined the hockey fraternity and sports lovers in grieving Shahid's death.
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"In the untimely & unfortunate demise of Mohammed Shahid, India has lost a talented sportsman who played with immense passion & vigour," Modi wrote on his twitter account.
"We tried our level best to save Mohammed Shahid but sadly, neither our help nor prayers were enough to save him. Tributes to him. RIP," Modi wrote in his second tweet.
"It is an irreparable loss and it is sad that great players are remembered only after have they have gone. I pray that God grants peace to his soul and strength to his family to endure the tough time," he added.
Remembering the time during the 1980 Games in Moscow, M K Kaushik, who was one of the closest friends of Shahid, said his team spirit was amazing.