Karlie Kloss and Josh Kushner Credit: Bryan Bedder/Getty Images; Andrew H. Walker/Getty Images

Sorry, guys: It appears that Victoria's Secret Angel Karlie Kloss is off the market.

After walking the runway in several super-skimpy getups, the flawless American-born supermodel, 20, hit an afterparty with a very lucky guy on her arm: NYC-based investor Joshua Kushner.

"They are really cute together," a source tells Us of Kloss and her handsome beau, a social gaming entrepreneur and venture capitalist who's pals with Ashton Kutcher (a successful dot-com investor in his own right).

At Lavo, the insider continues, the 27-year-old Instagram investor "seemed nervous and shy around everyone but handled it well. Karlie is stunning and the sweetest girl ever. She stuck close to him."

A rep for the Victoria's Secret model declined to comment.

From a powerful NYC family, Kushner's older brother is media mogul Jared Kushner -- who's married to Ivanka Trump.

Kloss has previously dated St. Louis Rams quarterback Sam Bradford. Kloss and fellow Angel Joan Smalls (who also walked during Wednesday's show) were recently named the new co-hosts of a revamped version of MTV's House of Style. The show premiered last month.