The distance between New York-based Thurman and London-based Busson has taken its toll, reported New York Post online.
Thurman, 43, started dating the multi-millionaire Busson, 51, who has dated supermodel Elle Macpherson, in 2007. However, in 2009 she returned an eight-carat diamond engagement ring a year after he proposed.
The pair worked through their differences and in 2011 were back together with Busson proposing again in 2012.
Thurman fell pregnant with their daughter, Rosalind Arusha Arkadina Altalune Florence Thurman-Busson, who she gave birth to in July 2012.
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"Uma and Arki were due to attend a gala together on April 8, but Uma showed up without her engagement ring or her fiance," the source said.
"Arki was scheduled to attend and it seemed clear there was only one reason why he didn't show - because he and Uma are no longer an item."
Thurman has two children with actor Ethan Hawke, Maya Ray, 13, and Levon, 10. Busson also has two children with Macpherson, Arpad Flynn Alexander, 14, and Aurelius Cy Andrea, nine.
Busson's spokesman was unavailable for comment, while a spokesman for Thurman declined to comment.