The law approved by a vote of 57 to 48 yesterday targets groups that receive more than half their funding from foreign governments or political organisations.
Hawkish groups in Israel largely rely on private donations, which are exempt.
The law requires the organisations to state that they rely on foreign funding in all communication with public officials and on TV, newspapers, billboards and online.
Lawmaker Robert Ilatov of the hard-line nationalist Israel Beitenu party says he co-sponsored the law because "intervention in Israel's internal affairs is not acceptable." Opposition lawmaker Nachman Shai says Israelis "will pay for this damage for many generations.