The left-back was named in Roy Hodgson's initial 23-man squad for the two fixtures but suffered the injury in Chelsea's 3-1 win over Norwich City on Sunday.
|12/1||England are 12/1 with BetVictor to draw 0-0 with Montenegro
Cole - who earned his 105th cap for England against Ukraine in September - underwent a scan on Monday morning although the extent of his injury is unknown.
Chelsea manager, Jose Mourinho, said of the injury on Sunday: "He is having this little problem for quite a while. He was feeling it hard in the ribs but I didn't [substitute] him because of that."
England currently top Group H by just one point following the 1-1 draw with Ukraine in September, and need to win both of their final group games to be sure of securing a place in next summer's World Cup.
Hodgson's side host Montenegro on Friday before Poland arrive at Wembley on October 15.