Iconic tenor Andrea Bocelli is in the middle of a crazy story that involves a wedding, his private estate in Italy ... and a $500,000 burglary!

Sources tell TMZ ... a couple from the United States was the victim of a robbery at a swanky Bocelli family estate in Forte dei Marmi -- an upscale seaside town on the Tuscan Versilia coast -- where intruders helped themselves to watches, cash, and fine jewelry, among other high-end brand valuables, while everyone was at dinner.

Sources tell TMZ the couple feels they were done dirty -- on the eve of their wedding, no less -- claiming there was no forced entrance into their locked and alarm-set villa. They say a wall safe, which they were unaware was in the home, was even cracked.

Local authorities responded ... but we're told the couple claims they did a half-ass job of investigating -- and their final report had glaring inaccuracies, like stating the villa was not locked, and the alarm was not set.

Sources close to the couple tell us ... reps for the property and Bocelli family essentially told them to kick rocks when they told them what occurred and demanded they be compensated for the traumatic burglary.

We're also told reps for the property responded with a cease and desist.

We reached out to Andrea and a rep for the estate ... so far, no word back.