The England international, who missed the entirety of last season due to a knee problem, last played in the 2-2 draw with Leicester City on October 17.
“Jay had the surgery last Tuesday and we are happy about that, because that was the best [thing] to do,” Koeman said at Thursday’s media conference ahead of the weekend trip to Manchester City.
“That was a good final decision to do that, but then you know he’s maybe out for seven to eight weeks.
“But we don’t have other injuries and the team is fit, the team is doing good training sessions and it’s always important to have a good feeling for Saturday’s game.”
Rodriguez has scored three times in 12 appearances in all competitions in 2015-16.