"He has passed away," a family member told PTI.
The 65-year-old Bollywood actor suffered a fatal heart attack on late Friday night. He was apparently here with his family for a concert.
His body will be brought to Mumbai later in the day after completing the formalities in Dubai.
Sheikh was born in Amroli in Gujarat's Baroda District. He was active in theatre before making his debut in Bollywood with M S Sathyu's 1973 Partition drama 'Garm Hawa' where he played the youngest son of Balraj Sahni. The movie is considered to be a pioneer of a new wave of Hindi art cinema.
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His most notable films include Ray's 'Shatranj Ke Khiladi', 'Noorie', 'Chashme Buddoor', 'Kissi Se Na Kehna', 'Katha', 'Faasle' and Sagar Sarhadi's 'Bazaar'.
He formed a successful pair with Deepti Naval working with her in 'Chashme Baddoor', 'Kissi Se Na Kehna', 'Katha' and most recently in 'Listen Amaya'.
Later on he acted in fewer films like 'Saas Bahu Aur Sensex', 'Tell Me O Khuda' and 'Lahore' for which he won the 2010 National Film Award for Best Supporting Actor for his performace as a boxing coach.