It was sixth time unlucky for Shankar as she is yet to register a win despite multiple nominations in the category over the years.
Yo-Yo Ma's "Sing Me Home" features tunes composed or arranged by different global artists as it examines the ever-changing idea of home.
The album was released to accompany a documentary on Ma's project entitled "The Music of Strangers: Yo-Yo Ma and The Silk Road Ensemble".
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Das, who was dressed in red kurta, said the ensemble sent a powerful message of unity and respect for each other's cultures.
"When things like this happen, it impacts us directly because a lot of us come from a lot of those countries," Das told reporters after accepting the award.
"Sing Me Home" won in a category that included Shankar's "Land of Gold", which is about the global refugee crisis.
The 35-year-old Indian musician was accompanied by her husband, British director Joe Wright at the music ceremony.
"Very excited that this man is my date to the #grammys today! It's the first time he's been free to join me. #husband #JoeWright #love," she had tweeeted ahead of the ceremony.
For the event, the musician chose a red, high-slit velvet Sabyasachi Mukherjee gown.
Shankar, the daughter of famous sitar maestro Pandit Ravi Shankar, received her first ever Grammy nomination at the age of 20 but she is yet to bag an award despite multiple nominations.