The Gladbach captain, who has won 11 caps for Germany and was joint top scorer with three goals in last year's Confederations Cup victory, badly twisted his left foot in the 35th minute of Saturday's match and was instantly taken off.
"It is very bitter to suffer the injury at this stage," Stindl said in a statement. "Now I cannot help my team in the crucial final matches of the season and my dream of the World Cup is also gone."
Gladbach are in ninth place with an outside chance of making the Europa League spots with two games remaining.
Stindl will undergo surgery this week and will be out for several weeks, the club said.
Defending world champions Germany are drawn in Group F along with Sweden, South Korea and Mexico for the tournament that starts on June 14 in Russia.
(Reporting by Karolos Grohmann; Editing by Toby Davis)
