The actress-turned-fashion designer, 27, sparked romance rumours with Schulte, who is the CEO of luxury eyewear brand Oliver Peoples, in September last year, reported Us Magazine.
The couple tried to keep their relationship under wraps.
"He was a great guy and cute, but it didn't work out," a source said.
Olsen's last high-profile romance was with 'Hangover' actor Justin Bartha, whom she dated from 2008 to 2011. Other exes include Elder Statesman designer Greg Chait and restaurateur Scott Sartiano.