MOSCOW—Russian opposition leader Alexei Navalny threatened protests and called for a nationwide boycott of next year’s presidential election after officials Monday ruled him ineligible to run against President Vladimir Putin.

“We are declaring a voters’ strike,” said Mr. Navalny, 41 years old, in a video released after the Central Election Committee announced it would bar him from the March 2018 election. “Going to the voting booth now is voting for lies and corruption.”

He...