Ottavia wrote a caption for the photo, reading: "Our little girl had her concert today. She was amazing. So strong and brave. She wore the boots you bought her."
She ended the note with a heartbreaking farewell to Bourdain: "I hope you are having a good trip, wherever you are."
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Ottavia, a Brazilian jiu jitsu competitor, was married to the 61-year-old TV star from 2007 to 2016. Bourdain was previously married to Nancy Putkoski from 1985 to 2005.
The celebrity chef, who took his own life at age 61, most recently was in a relationship with actress Asia Argento.
Bourdain began his ascent to fame in 1999 after writing a New Yorker article, "Don't Eat Before Reading This," which earned him a book deal to write 2000's "Kitchen Confidential: Adventures in the Culinary Underbelly."
He launched his TV career with "A Cook's Tour" on the Food Network in 2002, then joined the Travel Channel in 2005 to star in "Anthony Bourdain: No Reservations," which scored him two Emmys. In 2013, Bourdain moved to CNN to star in "Parts Unknown."