The Russian, who scored in last week's win over Hoffenheim, twisted his ankle after an aerial duel with team-mate Georg Niedermeier on Thursday.
Medical checks on Friday revealed the extent of his injury.
"I was doing extremely well and had fought my way back into the starting XI," said Pogrebnyak, 27, in a statement. "That is extremely bitter, but I will continue fighting."
His recent form helped Stuttgart, who narrowly avoided relegation last season, to fourth place after nine games, six points behind leaders Bayern Munich.
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