Billionaire Stephen Cloobeck's surprising arrest is tied directly to the criminal case surrounding his fiancée, Adva Lavie ... TMZ has learned.

TMZ broke the story ... Cloobeck was arrested Tuesday in L.A. on a felony charge connected to discouraging a witness from testifying, and we're told investigators believe that witness was tied to Lavie's ongoing theft case.

Lavie -- a former Penthouse Pet -- is accused of targeting wealthy men through dating apps and social circles ... allegedly stealing luxury goods, cash and personal information. She has pleaded not guilty to multiple felony charges.

According to prosecutors, Cloobeck attempted to dissuade or prevent 3 of Lavie's alleged victims from testifying against her.

He's also been charged with a misdemeanor for "annoying telephone calls" to a 4th man reportedly connected to her case.

The arrest marks a stunning escalation in the legal drama surrounding the billionaire businessman and his fiancée ... whose lavish Jerusalem wedding plans were already hanging by a thread after a judge ordered Lavie to surrender her passport and remain in California pending trial.

Cloobeck was booked Tuesday and later released on $300,000 bond. So far, neither he nor his attorney has publicly commented.