Major League Baseball approved the substitution Friday, shortly before Boston was set to face the Tampa Bay Rays in Game 2.
Richards, who was diagnosed with a left hamstring strain, will be ineligible for the rest of the division series as well as the AL Championship Series if the Red Sox advance. He would be eligible to return if Boston makes the World Series.
Richards made a brief appearance in Thursday's Game 1 loss to the Rays, retiring the only batter he faced on three pitches to end the second inning.
Barnes had 24 saves for the Red Sox this season, posting a 3.79 ERA with 84 strikeouts in 54 2/3 innings.