The site said that it is taking "aggressive steps" to remove such misinformation as part of its response to coronavirus hoaxes and false stories more generally.
But it will only take down those posts that are likely to cause physical harm, rather than any posts that include false claims about a link between phone masts and the covid-19 outbreak.
The conspiracy theory has spread widely across social media in recent days, after being amplified by a series of viral posts, celebrities and a widely popular petition.
"We are taking aggressive steps to stop misinformation and harmful content from spreading on our platforms and connect people to accurate information about Coronavirus," a Facebook spokesperson said.
"Under our existing policies against harmful misinformation, we are starting to remove false claims which link COVID-19 to 5G technology and could lead to physical harm. We will continue to work closely with governments and other tech companies to remove harmful misinformation and have partnered with health authorities like the WHO and NHS to connect people to the latest official guidance.”