Harder sustained the problem in Denmark's 2-1 friendly win over Switzerland on November 11.
A statement from Chelsea on Monday read: "Pernille has been reviewed at Cobham by the Chelsea medical team.
"Following that review and further discussion with a specialist, Pernille has undergone surgery and is expected to be sidelined for a significant period.
"Pernille will now begin a rehabilitation programme with support from the club's medical team. Everyone at Chelsea sends their best wishes to Pernille in her recovery."
Harder, who has scored six goals in six appearances for the Blues in all competitions this season, said in a Twitter post: "Saturday I underwent a successful operation on my hamstring.
"A time with recovery and rehabilitation now awaits before I can return to the pitch. It's never fun when those things happen but I'm ready to work hard and take on the challenge.
"No matter how hard it is with the injury, I will use it as an opportunity to come back in even better shape when I'm out on the other side. I feel lucky to be surrounded by so many talented people who I know will help me on the road back to recovery so I feel very safe."
Emma Hayes' defending champions are currently top of the Women's Super League, and also lead Champions League Group A ahead of Wednesday's home clash with Real Madrid.