The 'Life in a metro' star also posted a picture on Instagram where she is seen sitting next to Saroj Khan.
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The picture seems to have been taken during the shooting of the song 'Chura Ke Dil Mera' from the 1994 film 'Main Khiladi Tu Anari.'
Along with the picture, Shetty wrote about her first meeting with Khan.
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"A LEGEND has left us. Can't forget the moment I first met you when you came to choreograph 'Kitaabe' ( Baazigar) and I burst out crying (I was a huge fan of your work) I couldn't believe you were actually standing in front of me. Then came 'Churake dil', which was a milestone in my career... and many more," she wrote.
Remembering Khan, the 'Apne' actor noted, "You set the benchmark so high, taught me 'how' to express... a technician par excellence... No one shot women like you, you were the best!"
Extending her condolences to the family of the choreographer, Shetty wrote, "Will miss you. Churake dil mera #Saroj ji chale. May you rest in peace, Masterji. Strength and love to the family to cope with this irreparable loss."
Saroj Khan, the three-time National Award winner is credited with choreographing more than 2,000 songs.
Her list of credits include iconic numbers such as 'Dhak Dhak Karne Laga' from Beta (1992), 'Ek Do Teen' from Tezaab (1988), 'Hawa Hawai' from Mr India (1987) and many more.
Khan, who was earlier admitted to a hospital in Mumbai last month for breathing issues, passed away on Friday. She was 71.
She died due to a cardiac arrest in the ICU of Guru Nanak Hospital, where she was admitted on June 20.
The last rites of Saroj Khan will be performed at Malvani in Malad, Mumbai today.