The 51-year-old was sent to the stands by referee David Fernandez Borbalan at half-time of Barca's 3-1 defeat at Anoeta after remonstrating with the official in the tunnel.
Martino will subsequently have to take a watching brief from the stands when the Spanish champions host Almeria in La Liga on Sunday, with the club announcing they will not appeal the decision.
"The Argentine coach was sent off at half-time in the match against Real Sociedad and will not be allowed on the bench for the Almeria game," a statement published on Barca's official website read.
"FC Barcelona will present no appeal to the Appeals Committee."
The defeat at Sociedad leaves Barca second in the Liga standings, three points adrift of arch rivals Real Madrid.
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