The actor, who laid down the law as Uncle Phil, died on New Year's Eve aged 68. His publicist said he had suffered complications after heart surgery.
Jada used her Facebook page to post her reaction to the sad news.
"Happy New Year everyone! I was hoping to start the new year differently but we have lost yet another friend. James Avery who we all lovingly know as Uncle Phil from The Fresh Prince has passed," she said.
"Our condolences to aunt Florence (his mother), Miss Barbara (his wife) and all those who loved him. Rest in peace James."
Alfonso Ribeiro, who played his son on the show, said the world had lost "a truly special man".
Writing on Facebook page he added: "I am very saddened to say that James Avery has passed.
"Even though he played my father on TV, he was a wonderful father figure to me in life. He will be deeply missed."
The late actor grew up in Atlantic City, New Jersey and served in Vietnam with the US Navy before embarking on a thespian career.
Standing 6ft 5in, James was the heart of The Fresh Prince as Philip Banks, the wealthy patriarch who takes in Will's character and sees him getting in and out of scrapes.
His baritone voice meant he often got voiceover work notably as Shredder in the animated TV series Teenage Mutant Ninja Turtles. Other credits include Grey's Anatomy, NYPD Blues, Dallas and the film Fletch.
James' last screen outing is in Zach Braff's Wish I Was Here, which is scheduled to premiere at the Sundance Film Festival.
The actor and director described him as "very funny and smart". "He did a cameo as a favour to me in WIWH and had the entire set rolling with laughter," he said.