The Dreamgirls star also shared a throwback photo of her and her mum from the last election she voted in.
"The last thing my mother did was go vote for Obama! So it's odd that I would run across this picture on Election Day, the day after her birthday n she's wearing a shirt saying "vote your choice " IM WITH HER ... well mommy I already did , Pls vote today guys !!!," she wrote.
In October 2008, the Oscar winner's mother, who was 57 at the time, her 29-year-old brother, Jason, and her 7-year-old nephew, Julian King, were shot dead in Hudson's childhood home.
Hudson's ex brother-in-law, William Balfour, was later found guilty of the murder.