Senderos dislocated his shoulder while playing for Switzerland at the World Cup last month and it was initially thought that the 21-year-old would be out for six weeks.
But Arsenal manager Arsene Wenger confirmed that his defender will be sidelined for a longer period.
"We've lost Senderos for the next three months, Johan Djourou and Gael Clichy have injuries as well," Wenger told Arsenal's official website on Monday.
With Senderos' injury and English international defender Sol Campbell heading out of the Emirates Stadium, Wenger may be forced to look for a substitute in the transfer market ahead of the new season's start.
"If we find a player who can play at centre back or left back, then we are still open for transfers."
Senderos was a starting member Arsenal's defense that made history by keeping a clean sheet for ten consecutive games in the UEFA Champions League last season.