In a letter posted on Twitter, Mr Schumer called it "deeply troubling" that personal data of US citizens could go to a "hostile foreign power".
Privacy concerns have been raised about the Russian company which developed the app after it went viral in recent days.
FaceApp has previously denied the allegations.
Wireless Lab, a company based in St. Petersburg, says it does not permanently store images, and does not collect troves of data - only uploading specific photos selected by users for editing.
"Even though the core R&D team is located in Russia, the user data is not transferred to Russia," a company statement reported by news site TechCrunch said. Mr Schumer however has asked that the FBI and the Federal Trade Commission (FTC) investigate FaceApp.
"I have serious concerns regarding both the protection of the data that is being aggregated as well as whether users are aware of who may have access to it," his letter reads.
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