The move follows violence at a match between rivals Olympiakos and Panathinaikos, as well as a brawl between club officials at a board meeting on Tuesday.
The Greek league has already been suspended twice this season due to violence.
Newly-elected ruling party Syriza have pledged to stamp out the problem.
The suspension affects the top three divisions in the country.
"What we have been informed is that the Super League and the Football League have been suspended indefinitely," Super League president Giorgos Borovilos told reporters.
"We have a new government who are looking to bring this subject up for discussion and implement state laws related to it."
Imagine if due to the racist chelsea supporters incident the other day, that Premiership, Championship and League 1 games all got banned indefinitely, cause chaos!
