According to the report, a member of Schumer's staff hacked into the Twitter account of a colleague who was also sharing the same WiFi network to demonstrate how it's done.
"The bottom line is, if we let this proliferate, everyone is going to pay the price," Schumer said. "It could become the leading cause of identity theft."
Facebook spokesman Andrew Noyes said security is a top priority for Facebook, which is why the site rolled out an HTTPS option for users last month.
"We encourage people to consider enabling this option if they frequently use Facebook from public Internet access points," Noyes said.
"These features are especially useful when you're uncertain whether your network or computer is secure. Security is an arms race, and our teams are always working to identify the next threat and build defenses for it."