Both the national team and clubs are covered by the ban, handed down because the Greek FA had broken rules on "the independence of members and decision-making in each country".
The suspension will be in place with "immediate effect and until further notice", according to a Fifa statement.
A spokesman for the Greek FA said the verdict was unexpected.
"Fifa's ruling deals specifically with the independence of the national federation but it is a very complicated issue.
"We, of course, hope for a quick and favourable solution to this problem for the good of Greek football,” he said.
Fifa said that it had issued several warnings to the HFF to guarantee, by a 15 July deadline, that the running of football in the country would be free from political movement - but this had been ignored.
