Paraguay international Barrios, who had only recently returned from an injury that saw him miss the start of the season, broke off training on Monday and tests showed a minor muscle injury.
“Lucas Barrios will remain in Dortmund along with Patrick Owomoyela,” Dortmund said before departing for Athens.
Owomoyela, who is also just back from a long injury break, suffered a partial muscle tear in their 2-0 win over Werder Bremen on Friday.
Dortmund are third in Group F with one point from two games, ahead of Olympiakos, who lost both their opening games. Olympique Marseille lead the standings with six points, two ahead of Arsenal.