News reports last month revealed that some apps in the Apple Store had collected users' address books without their knowledge, despite the fact that such data collection violates Apple's policy.
Last week, The New York Times reported that Apple and Android apps could also access users' private photos.
Schumer said that even if Apple and Google policies prohibit apps from accessing users' private information, "it is not clear whether or how those terms of service are being enforced and monitored."
A Google spokeswoman explained that apps do not need permission to access photos because most phones used to store images on a removable memory card.
"As phones and tablets have evolved to rely more on built-in, non-removable memory, we're taking another look at this and considering adding a permission for apps to access images," the spokeswoman said. "We've always had policies in place to remove any apps on Android Market that improperly access your data.”
In his letter, Schumer noted that FTC Chairman Jon Leibowitz has focused on enforcing online privacy protections.
"Specifically, I hope you will consider launching a comprehensive investigation to explicitly determine whether copying or distributing personal information from smart phones, without a user’s consent, constitutes an unfair or deceptive trade practice," he wrote. "In addition, I believe smartphone makers should be required to put in place safety measures to ensure third party applications are not able to violate a user’s personal privacy by stealing photographs or data that the user did not consciously decide to make public."
The FTC reached settlements with Google and Facebook last year over charges that the Web companies violated their own privacy agreements.
—Updated at 1:50 p.m.