A video posted to the venue's YouTube page shows 14-year-old Maya Thurman Hawke singing at the Jones Street club and restaurant on Saturday while her father played guitar, Jeremiah's Vanishing New York first reported.
Maya Thurman Hawke sang the Townes Van Zandt song "No Place to Fall" in her performance, which Caffe Vivaldi advertised online as a performance by "Maya" — excluding the singer's famous last name.
Ethan Hawke, 41, and Thurman, 42, married in 1998 and divorced in 2004 after having two children — Maya and younger brother, Levon.
Thurman has been notoriously press-shy and has kept a low profile since fending off a repeated stalker who was convicted of harassing her with threatening phone calls and letters to her Manhattan home.
Musician John Schmitt, who performed at the venue later that night, tweeted about the celebrity spotting.
"So Uma Thurman and Ethan Hawke are at Vivaldi right now. No big deal," he wrote.