'Hamilton' Musical Suing Over Stolen Logo!

The logo for "Hamilton: An American Musical" is now so iconic, it's become a target for rip-off artists ... according to producers behind the massive Broadway hit.

The head honchos of the company that runs all things 'Hamilton' just filed suit against t-shirt makers, SunFrog, for hawking bootleg 'Hamilton' shirts on their site.

In the docs -- obtained by TMZ -- 'Hamilton' heads say SunFrog and a company called GearLaunch are using the famous silhouetted image of Alexander without permission.

Lawyers for the musical aren't buying GearLaunch's excuse -- that they assume freelance t-shirt designers have legally obtained rights to all the images beforehand.

They're suing to halt all sales and marketing of the alleged phony merch, and to get all profits.

SunFrog's legal team tells us, "As an online platform and service provider, there may be instances where user-generated content on our platform doesn't fully comply with either our terms and conditions or intellectual property law in general."

However, they say they do take intellectual property rights very seriously.