The two-time American League Cy Young Award winner was given the nod Saturday by manager Terry Francona.
Stan Coveleski is the only other Cleveland pitcher to start five straight openers. Bob Feller holds the franchise mark with seven Opening Day starts overall. Kluber is the first to earn five Opening Day assignments with the Indians since CC Sabathia from 2003 to 2008.
Kluber will take the ball Thursday at the Minnesota Twins.