The Fashion Police producer thanked well-wishers for the "kindness and support" they had shown her and her 13-year-old son Cooper in the weeks following Joan’s death on 4 September.
Writing in a WhoSay post on Wednesday evening, Melissa said, "As my son Cooper and I mourn the loss of my mother, we want to thank everyone for the beautiful cards and flowers conveying heartfelt messages and condolences, which continue to arrive from around the world and through social media.
"My mother would have been overwhelmed by the scope and depth of the love that people have expressed for her. It is certainly helping to lift our spirits during this time.
"We are forever grateful for your kindness and support in continuing to honour my mother's legacy, and for remembering the joy and laughter that she brought to so many."
Comedienne Joan, 81, was rushed to hospital on 28 August after going into cardiac arrest during surgery on her vocal chords at a private clinic.
She had been on life support for almost a week at New York's Mount Sinai hospital before passing away.
The star, who paved the way for a new generation of funny women, was celebrated at a star-studded funeral on 7 September, attended by the likes of Whoopi Goldberg, Sarah Jessica Parker and Donald Trump.