The firm was accused of improperly obtaining personal information on behalf of political clients.
According to Facebook, data about up to 87 million of its members was harvested by an app and then passed onto the political consultancy.
The social network said its own probe into the matter would continue.
"This doesn't change our commitment and determination to understand exactly what happened and make sure it doesn't happen again," said a spokesman.
"We are continuing with our investigation in cooperation with the relevant authorities."
Clarence Mitchell, a spokesman for Cambridge Analytica, referred the BBC to a statement on the firm's website.
"Over the past several months, Cambridge Analytica has been the subject of numerous unfounded accusations and, despite the company's efforts to correct the record, has been vilified for activities that are not only legal, but also widely accepted as a standard component of online advertising in both the political and commercial arenas," it said.
"Despite Cambridge Analytica's unwavering confidence that its employees have acted ethically and lawfully... the siege of media coverage has driven away virtually all of the company's customers and suppliers.
"As a result, it has been determined that it is no longer viable to continue operating the business."
The statement added that its parent company SCL Elections was also commencing insolvency proceedings.
Cambridge Analytica's chief executive Alexander Nix was suspended in March after secretly being recorded by Channel 4 News.
In the video he suggested that the London-based firm had helped run Donald Trump's digital election campaign. He also detailed ways that it could discredit other politicians, including sending "girls around to the candidate's house".
Cambridge Analytica subsequently said that it had only licensed 30 million records belonging to US citizens from the data-collecting app's creator Dr Aleksandr Kogan, and that they had not been used it in the US Presidential Election.
The firm added that it had since deleted all the information despite claims to the contrary by others.
In testimony to Congress about the scandal, Mr Zuckerberg had said that his personal details were among those that had been harvested.