Not anymore. The only authentic male burlesque show we've known of was at Ivan Kane's Forty Deuce at Mandalay Bay, which was briefly home to a male review called Stormy Monday. It performed every Monday but closed at the end of April this year. A call to the venue confirmed that there are possible plans to bring back another male show, but they had no idea of the time-frame. Since the original Ivan Kane's Forty Deuce in Hollywood recently closed its doors (Mr Kane has a new venture called Cafe Wa s [sic.]), we're wondering what's in store for the Vegas venue, although we haven't heard anything to suggest that it might be in any trouble.
For those who aren't familiar with the burlesque tradition, it was actually an English musichall performer named Lydia Thompson who, together with her troupe of blond beauties, introduced the genre to the U.S. in the 1860s. While in its latter days burlesque became synonymous with striptease, in its original incarnation it was a lower-class form of entertainment, often somewhat improvised, that made fun of ("burlesqued") the opera, theater, and other social habits of the upper classes, and came to feature scantily clad, shapely, and suggestive ladies to help keep the audiences engaged in an era when even piano legs were being covered up for being lewd.
As burlesque found itself competing with vaudeville, movies, and radio in the early twentieth century, the strip-tease element became more pronounced and some performers, like Lili St Cyr, Tempest Storm, Gypsy Rose Lee, and fan dancer Sally Rand turned it into an artform. But legal crackdowns in the 1920s-'30s signaled the death knell for burlesque until its revival in the 1990s by performers nostalgic for the spectacle and glamor of the old times, with venues like Sally's Hideaway in Times Square popping up and contemporary performers like Dita von Teese.
As far as male burlesque, or "boylesk," is concerned, it has its roots in the female version and makes similar use of the same elements of dance, costume, sets, lighting, and the removal of clothing to emphasize male sexuality. Our research pulled up one Eugene Sandow as the first nude male superstar, who in the 1890s exhibited himself with a fig leaf as a physical culturist. The beginning of male burlesque was born in Paris music halls like the Lido in the 1930s, but the male dancers were in duos doing apache and flamenco acts as accessories to the women. The, in the '50s, New York started to spawn underground venues like "Club 82," which featured solo male strippers, but its heyday was really the mid-'60s to '80s and it's never taken off like female burlesque.
So, there's the long answer to your question, which is that there's currently no authentic male burlesque show in Las Vegas and no sign of any new one opening in the foreseeable future. There are some options, however, aimed both at female and gay male audiences, if you're desirous of seeing men removing their clothing. Here's what's currently on offer: