The campaign, created by Viacom Brand Solutions, is due to break on Monday and was filmed at the New London Theatre last week.
The spot features clips from the show with shots of the Blue Men jumping around and covering children with paint.
The campaign is supported by a specially created microsite on the website. Blue Man is giving away free children's tickets through a Nickelodeon ticket hotline.
There is also a competition element whereby children enter online to win a trip to London to be a Blue Man for the day.
In March, the 'Blue Man Group', which is currently performing at the New London Theatre, sponsored ITV's LWT London weather bulletin in a six-figure deal to showcase its comic sketches.
The sponsorship ran until last month and was supported by TV ads in the London area, during programmes such as 'Coronation Street', 'CD:UK' and 'Celebrity Stars in Their Eyes', as well as press and outdoor ads.
The US theatre company, which was founded in 1982 and went on to appear in an Intel Pentium III campaign in the late 1990s, opened its London show in November at the New London Theatre.
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