WASHINGTON—Herman Cain withdrew from consideration for the Federal Reserve Board on Monday, saying he did so primarily because of the salary, not the Senate opposition he faced, in a setback for President Trump’s efforts to place a political ally on the central bank.

“It’s an honor, it’s prestigious, and I really wanted to do it, emotionally,” Mr. Cain said in an interview Monday, a few hours after informing the White House of his decision. “But factually, it is a big cut in pay,” he said, referring to the $183,100 annual...