Foden will see a specialist on Wednesday, but his immediate prospects do not look good.
In a statement, Northampton said: "Ben Foden sustained significant damage to his ankle ligaments during last Friday's Aviva Premiership game against Bath, and he is going to see a specialist tomorrow.
"The club will have more information after that, but Ben is expected to be out of action for a number of weeks."
England's next Test is against Fiji on November 10 followed by games against Australia, South Africa and New Zealand over the next three weekends. All four matches are at Twickenham.