The "Republican" button allows users to switch to a homepage view that blocks out stories about the birth and replaces them with non-monarchy focused articles.
It introduced a similar button to screen out coverage of William and Kate's wedding in 2011, and for the Queen's Diamond Jubilee in 2012.
The paper's regular home page displayed a lead story this morning titled, "Duchess of Cambridge admitted to hospital in early stages of labour" .
The Guardian acknowledged the royal birth as a "major news story", but said some of its readers would not be interested in the round-the-clock coverage provided by much of the mainstream media.
A Guardian News & Media spokeswoman said: "While the birth of a new heir to the throne is a major news story, we know some of our readers would rather read a little less of our comprehensive coverage than others.
"So, as with the royal wedding and the Diamond Jubilee, we've offered them the chance to hide royal baby news from our desktop website homepage with our Republican/Royalist button."
The Duchess of Cambridge went into labour this morning and is at St Mary's Hospital in London.