The couple were linked in late November after being spotted spending time together at Naomi Campbell's birthday in India.
They were later spotted publicly together several times, but Page Six reports that trouble arose when Moore joined Schnabel in Miami while he was meeting with major art buyers.
An insider told the publication: "Vito has worked very hard to be taken seriously in the art business, and doesn't want to be seen as somebody who dates celebrities. He hated having photographers follow him around after word got out about him and Demi.
"Vito wasn't too happy that Demi flew down to party at Art Basel [in Miami] while he was working to build his business. It was a distraction he didn't need while all the big collectors were in town."
Moore was later photographed partying with rocker Lenny Kravitz, Stacy Keibler and others at a celebrity event in Miami.
She is currently in the midst of divorce proceedings with Ashton Kutcher, with whom she split in November 2011.