According to the company, the Trending box has been available in only five countries - the U.S., Canada, U.K., India and Australia - and accounts for less than 1.5% of clicks to news publishers on average.
The Facebook logo is seen at the Nasdaq MarketSite in New York's Times Square.
Facebook said "Trending" will be removed next week.
The contractor claimed Facebook downplayed conservative issues and promoted liberal causes. Facebook's Alex Hardiman explained, "So we're exploring new ways to help people stay informed about timely, breaking news that matters to them, while making sure the news they see on Facebook is from trustworthy and quality sources".
Mark Zuckerberg, Facebook's CEO, later met with conservative commentators and leaders to defuse an uproar over the allegations.
The trending section had been a headache for the company.
The company Friday said the feature, which it intends to remove next week, became less useful over time, and that removing it would "make way for future news experiences" on the platform.
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The breaking news label that Facebook is testing with 80 news publishers will let outlets such as the Washington Post add a red label to indicate that a story is breaking news. More problematic was the feature's tendency to spread fake news, particularly during the 2016 presidential election, The Associated Press noted.
We introduced Trending in 2014 as a way to help people discover news topics that were popular across the Facebook community.
"There are other ways for us to better invest our resources", Hardiman said. These efforts will be funded by Facebook itself, the company said.
The company instead said it will explore new news related projects like letting publishers include a "breaking news" label on their posts in Facebook's newsfeed.
One reason the feature is so little used could be that it's not immediately visible on Facebook's app or mobile version, where most people use the site.
Today In: We're testing a dedicated section on Facebook called Today In that connects people to the latest breaking and important news from local publishers in their city, as well as updates from local officials and organizations. Facebook Watch will soon have a dedicated section for live news coverage.