CEO of Twitter and Square Jack Dorsey accepts the award for CEO of the Year onstage during the Thurgood Marshall College Fund 28th Annual Awards Gala at Washington Hilton on November 21, 2016 in Washington, DC.

Shares of Twitter and Snap fell on Tuesday, as rival Facebook faced further backlash over a privacy breach of user data.

Twitter shares were more than 10 percent Tuesday, and Snap shares were more than 2.5 percent lower. (Facebook fell also fell about 2.6 percent, a day after tumbling another 6.7 percent.)

It's unclear why Twitter and Snap dropped so sharply, but their rival for ad dollars — Facebook — has been stung by a report from The New York Times and The Guardian over the weekend that alleged that a data firm, Cambridge Analytica, improperly gained access to the data of more than 50 million Facebook users. That report and those that followed have gotten the attention of state regulators and congressional intelligence committees, commerce committees and judiciary committees. The FTC may also be probing Facebook.

Heath Terry, lead internet research analyst at Goldman Sachs, told CNBC on Tuesday the reports could impact the growth story of Facebook, which makes money off digital ads, just like Twitter and Snap. Prior to the breach revelations, Facebook's leadership had committed to increasing spending on security.

Twitter, though, is also the subject of regulatory scrutiny elsewhere. The Israeli government is considering legal action against Twitter over failure to remove content from "terrorist organizations," Bloomberg reported.

Earlier this month, Twitter CEO Jack Dorsey solicited proposals on how to improve Twitter's ability to address abuse faster on the platform. Twitter shares are still up more than 100 percent over the past year.

Still, another digital advertising provider, Google, didn't see a big stock decline on Tuesday. There hasn't been reporting linking Twitter or Snap to the Cambridge Analytica allegations.

— Additional reporting by CNBC's Tae Kim.