The former heads of the air force and navy were among those detained in raids in Istanbul, Ankara and Izmir.
The so-called "sledgehammer" plot allegedly involved planting bombs in mosques to destabilise the government.
The head of the army has dismissed the allegations, insisting coups in Turkey are a thing of the past.
The army has overthrown or forced the resignation of four governments since 1960 - the last time in 1997.
The men arrested include the former air force chief Ibrahim Firtina, former navy chief Ozden Ornek, and several other generals and colonels, both serving and retired, Turkish media outlets reported.
The head of the army, General Ilker Basbug, postponed a trip abroad in the wake of the arrests, media reported.
The investigation follows reports published in the liberal Taraf newspaper.
Taraf said it had discovered documents detailing a plot laid in 2003, to bomb two Istanbul mosques and provoke Greece into shooting down a Turkish plane over the Aegean Sea, in a bid to undermine the Turkish government and justify a coup.
The army has said the plans were actually part of a planning exercise at a military seminar, and not a coup plot.
The alleged plot is similar, and possibly linked, to the reported Ergenekon conspiracy, in which military figures and other staunch secularists allegedly planned to foment unrest,leading to a coup. Dozens of people are already on trial in connection with that case.
Many Turks regard the cases as the latest stage in an ongoing power struggle between Turkey's secular nationalist establishment and the governing AK Party.
The AKP has its roots in political Islam, and is accused by some nationalists of having secret plans to turn staunchly secular Turkey into an Islamic state.
The government rejects those claims, saying its intention is to modernise Turkey and move it closer to European Union membership. BBC