In a statement the Greek General Secretariat for Sports said European football's governing body (UEFA) had forwarded a list of suspect matches.
The file, sent to the General Secretary for Sports Panos Bitsaxis, lists 15 matches and, as well as the four top division clubs, also refers to eight from the Second Division and one from the third. One Greek Cup match is also under suspicion.
"UEFA regularly monitors every match played throughout Europe and we regularly notify member assoiations of matches that we suspect could be subject to match-fixing," a UEFA spokesman said. "This is what we have done this week in sending a file to the Greek authorities."
The Greek statement said a criminal investigation had been ordered and a file forwarded to the Athens prosecutor.
"The documents refer to four teams, which during the 2009-2010 season competed in the Super League, eight teams competing in the Second Division and one team which competed in the third division," it said.
A similar investigation is already underway based on a previous file sent by UEFA, including 27 suspicious matches from the 2008-09 season.
The controversy is the latest to beset Greek soccer following match-fixing scandals in 2004, 2006 and 2009.
