The 26-year-old broke down in training yesterday and a hospital scan revealed he has strained his calf and is also suffering with a back injury, so joins defender Patrick Owomoyela in missing the Group F match.
The new injury is the latest setback for Barrios, who had previously been sidelined for just short of two months with a thigh injury he suffered in July during the final of the Copa America.
Having scored 16 goals in 32 league appearances last season, Barrios played a key role in Dortmund winning the German league title in 2010/11, but has yet to complete a Bundesliga game this season.
Dortmund's attack against Olympiacos will be led by Poland striker Robert Lewandowski, who already has five league goals this season.
The German champions will welcome back defenders Marcel Schmelzer and Lukasz Piszczek, who both missed last Friday's 2-0 win over Werder Bremen in the Bundesliga, but Dortmund know they face an uphill task in Greece. After being beaten 3-0 at Marseille in their last Champions League match, defeat is not an option.
"If we want to play a good role in the group, we have to win this game," said midfielder Sven Bender with Dortmund third in the group behind Marseille, who are top after two wins, while Arsenal are second. "We know that it is a difficult group, but we also know that we can match the other teams."