MAGDEBURG, Germany—The night after Donald Trump won the presidency, hundreds of backers of an anti-immigrant party whose success has shaken German politics gathered in the biting cold in this eastern German city and celebrated a new reality.

“Bravo, Mr. Trump, you get it!” state party leader André Poggenburg shouted from the stage last Wednesday, framed by the dark hulk of a 500-year-old Gothic cathedral. “Today, I must say, it is truer than ever: Merkel must go!”

“Merkel muss weg! Merkel muss weg! Merkel muss weg!“ the crowd chanted in response. “Merkel must go!”

Mr. Trump’s election is the second upset populist victory in the West this year, after last June’s antiestablishment Brexit vote in the U.K. With it, German Chancellor Angela Merkel, Europe’s most influential defender of postwar internationalism, finds herself further under siege.

The Continent’s populist tide has reached Austria, where an anti-immigrant candidate is polling strongly ahead of next month’s presidential election, and Italy, whose center-left premier could lose a constitutional referendum on which he has staked his career. Aides to Ms. Merkel think in France, nationalist, anti-immigration leader Marine Le Pen could win next year’s presidential election. At home, lingering discontent with Ms. Merkel’s handling of the refugee crisis could spoil her Christian Democratic Union’s re-election bid next fall.