Facebook Inc. said it suspended Cambridge Analytica, a data firm that helped President Donald Trump with the 2016 election, after learning that it misled the social-media giant and violated its policy for handling user data.

Facebook said late Friday that it been given information that Cambridge Analytica, along with two individuals who don’t work there, improperly kept Facebook user data for years despite telling the social network that it had destroyed those records. Facebook didn’t say how Cambridge Analytica used that...