The NFF said seven Burkinabe players failed to secure British entry visas, forcing Monday’s match at Barnet in north London to be shelved.
The Super Eagles were using the match as part of preparations for their remaining qualifiers for the World Cup 2018 and Africa Cup of Nations 2019.
NFF official Chris Green said the cancellation was “no fault of either the organisers or the Nigeria Football Federation”.
“We will announce further plans for the Super Eagles’ preparation for these two important qualifying campaigns in due course,” he added.
Burkina Faso officials were told of the visa issues late on Friday.
On Thursday, Nigeria drew 1-1 with Senegal in the first of its two scheduled friendly matches in the British capital.
Morocco beat Burkina 2-0 in a friendly in Marrakech on Friday.