Late Sridevi was named the Best Actress for her role as a vengeful mother in the Hindi film "Mom".
Her husband and two daughters are overjoyed and said the legacy of the "super actor" will live on.
Sridevi's husband Boney Kapoor and daughters Jahnvi and Khushi expressed their happiness in a joint statement.
Sridevi died in February in a Dubai hotel.
Filmmaker Shekhar Kapur, jury chairperson for the 65th National Film Awards, told the media that his "Mr. India" actress Sridevi wasn't chosen for the honour because of his relationship with her but due to her contribution to "Mom".