Manager Rob Thomson said Robertson strained his right calf jumping up in the air when Bryce Harper homered against the Cardinals in the last round.
The Phillies beat the Braves 7-6 in Game 1 on Tuesday in Atlanta.
"He's devastated," Thomson said of Robertson, according to the Philadelphia Inquirer. "He knows how big a part he is to this club."
The 37-year-old Robertson was effective for the Phillies after an August trade from the Cubs -- posting six saves in 11 games with a 2.70 ERA. He threw one inning against St. Louis in Game 1 of the wild-card series and picked up a win.
The Phillies used a closer-by-committee approach for a chunk of the season. Nobody on the team had more than 12 saves. Converted starter Zach Eflin picked up his first save in Game 2 against the Cardinals but he struggled in Tuesday's opener against the Braves, allowing three runs in the ninth before escaping any further trouble.