According to a report in The Wall Street Journal late on Friday, the social media giant was investigating whether the analytics firm's "contracts with the US government, a Russian non-profit organisation tied to the Kremlin and the Turkish government violate the platform's policies".
Crimson Hexagon has reportedly collected more than 1 trillion public social media posts from Facebook, Instagram, Twitter, Tumblr and other online sources.
The company has had contracts in recent years to analyse public Facebook data for third-party clients, the report claimed.
It was co-founded by Harvard professor Gary King in 2007 who now leads Facebook's independent research initiative titled "Social Science One" which is focused on preventing election interference, said the report.
"We are investigating the claims about Crimson Hexagon to see if they violated any of our policies," Ime Archibong, Facebook's Vice President of Product Partnerships, said in a statement.
Facebook, however, said the firm didn't inappropriately obtain any Facebook or Instagram user data, adding that using the data for surveillance is a violation of the company's policies.
"We do not collect private data from social media providers or anyone else," Crimson Hexagon's Chief Technology Officer Chris Bingham said in a blog post.
"Crimson Hexagon only allows government customers to use the platform for specific approved use cases; and under no circumstances is surveillance a permitted use case," Bringham wrote.
According to Crimson Hexagon, it uses technologies including Artificial Intelligence (AI) to help clients get insights and shape marketing campaigns and develop new products.
In a statement to the portal Fast Company, King said: "Even though he is co-founder and board chairman, he has never had day-to-day involvement in Crimson Hexagon."
In April this year, Facebook had warned investors that more users' data scandals in the future may adversely affect the social networking giant's reputation and brand image.
In its quarterly report, Facebook said that its ongoing investments in safety, security, and content review will identify additional instances of misuse of user data.
"We may also be notified of such incidents or activity via the media or other third parties," Facebook said.
Appearing before the US Congress, Facebook CEO Mark Zuckerberg told the lawmakers that his own personal data was part of 87 million users' that was 'improperly shared' with the British political consultancy firm Cambridge Analytica.
Facebook warned investors that there may be more such data breaches in the future.