Foden will undergo surgery after sustaining the injury during Northampton's Premiership match against Bath last Friday.
"It is unfortunate for Ben who has had a good run in the side and is a valuable leader," England coach Stuart Lancaster said in a statement on the RFU website.
"But we have a number of back three players who are playing well and this offers a chance for them. I am sure Ben will be available for the Six Nations."
England play Fiji on November 10 before taking on Australia, South Africa and New Zealand.