The 74-year-old Spaniard, considered the world's most famous living opera singer, had been scheduled to conduct Puccini's Tosca, which opens on Friday.
But Domingo - who has had a series of health scares in recent years - was admitted to a hospital on Tuesday after suffering inflammation of his gallbladder and will undergo an operation early next week, the Met said.
"It is expected that this minimally invasive procedure will allow him to resume his activities after a brief hospital stay," the Met said in a statement.
Domingo plans to return to the Met to conduct on November 6th, it said. The opera house had initially advertised his return date as November 2nd.
Conductor Marco Armiliato, a veteran of Met opera productions, will step in for Friday's season premiere, with another Italian, Paolo Carignani, leading three performances later this month.
In 2013, Domingo was hospitalized in Spain for the blockage of a lung artery, and in 2010 he underwent surgery for colon cancer.
But Domingo maintains an active schedule and is due in April to return to the Met to sing in Verdi's "Simon Boccanegra."