In English, the precursor to "belly button" is "navel" -- Middle English "navel"/"navele", from the Old English "nafela", which in turn comes from proto-Germanic language roots. Indeed, the use of "navel" continued on past the invention and popularization of buttons -- buttons as garment closures (the kind with a shaft rather than a flat back) were popularized in the 13th century. "Belly button" only dates back to the second half of the 19th century, apparently as American slang. Green's Dictionary of Slang gives it the according definition:

[mid-19C+] (US) the navel, esp. in juv. use; thus my belly button is playing hell with my backbone, I am very hungry

Its proliferation in print is a 20th century phenomenon, not only because the navel was a difficult topic of discussion outside medical contexts in the 19th century but likely also because of the general proliferation of phrases that in the century prior had been only suitable for spoken slang.