The star took to Twitter this morning (July 1) and posted "Goodbye #grangranDOLLY get your beauty rest until I see you".
Brathwaite had battled cancer for months and Rihanna had previously shared pictures of her visits to Memorial Sloan-Kettering hospital, where her grandmother was being treated.
After posting a string of images, including a picture holding her late grandmother's hand, the 'Umbrella' singer retweeted a message from a fan who expressed sympathy for her loss.
"A little tribute true and tender. just to show that we remember. time may pass and fade away. but memories of you will always stay. (sic)"
Rihanna had earlier been criticised for a performance she gave at Sweden's Peace and Love festival. She headlined the event yesterday evening before news of Brathwaite's death became public, and the Daily Mail reports that festival-goers described her lacklustre set as "disgusting and shameful".
Others claimed she appeared to be drunk after she forgot which country she was in and dedicated 'Redemption Song' to Norway following the right-wing attacks that killed 77 people last summer.
Rihanna is scheduled to perform at Rock in Rio in Madrid, Spain on July 5 and at the Barclaycard Wireless Festival in London next weekend. She was recently in the capital filming for her new fashion show with Sky Living.
Watch the video for Rihanna's latest single 'Where Have You Been?' below: