Speaking to The Times, Fallon said the EU's plan to create a "common military force" is "not going to happen".
France and Germany have put together a timetable for establishing an EU army to rival Nato. A document on the army was discussed at a summit in Bratislava that Britain was not invited to. The European Commission will make proposals for the common military force in December and is looking to get an agreement by June next year.
We are full members of the EU and we will go on resisting any attempt to set up a rival to Nato.
We have always been concerned about unnecessarily duplicating what we already have in Nato.
Creating an EU army has been an ambition of the German defence secretary Ursula von der Leyen for some time. Due to Germany's Nazi past, it has long taken a passive stance on international conflict, but an EU army would be a vehicle through which the Germans could act abroad.
Given Britain's recent decision to leave the EU, it would be hard for Fallon to influence the EU's decision on a joint military force. Although Germany has signalled that it will maintain a civil attitude towards Britain after the Brexit vote, other EU representatives have taken a more hard line stance.
At the summit in Bratislava, Donald Tusk, president of the European Council, said the EU will "respect the needs of our British colleagues" but that Brussels "must protect the interests of the remaining 27 states."
Slovak prime minister Robert Fico said: "I will be perfectly frank. Unlike the UK, we know what we want. Our position is clear. We will not allow this negotiation to damage our interest.
"You cannot get away from feeling that such negotiations run the risk of creating second-class citizens in the UK. That will be a crucial point for us in negotiations."