He also insisted that Britain's own role in NATO was not in question whatever the result of the referendum, despite uncertainty over the fate of its Scottish-based nuclear deterrent.
Rasmussen told an event hosted by the Carnegie Europe think-tank in Brussels that he was "not going to interfere with the referendum campaign in Scotland".
But he added: "If a new independent state wants to become a member of NATO it will have to apply for membership of NATO.
Rasmussen would not estimate how long it would take to decide on new membership, saying it depended on the country and their "ability to fulfil the necessary criteria".
The Dane added that it was a "hypothetical question" and that NATO's 28 members "haven't discussed it at all".
Britain's nuclear Trident armed-submarines, based at the Faslane naval base in Scotland, are part of NATO's collective deterrent and have long underpinned London's diplomatic and military power.
Asked if Scottish independence affects Britain's role in NATO, Rasmussen said: "Again without interfering with the debate leading up to the referendum, I don't see that any outcome of the Scottish referendum will have an impact on the UK's contribution."
The European Union has also insisted that any newly- independent nation such as Scotland emerging from a existing member state would also have to reapply for membership.
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