WASHINGTON—The Department of Homeland Security is suspending enrollment in Global Entry and other trusted-traveler programs for New York residents in response to the state’s so-called sanctuary policies to safeguard immigrants from deportation, the acting chief of the department said.

Chad Wolf announced the decision in a Fox News interview Wednesday, a day after President Trump devoted several minutes of his State of the Union address to excoriating sanctuary jurisdictions, which limit law-enforcement cooperation with U.S....