Its claimed opposition politicians with links to Moscow are behind the alleged coup. The relationship between Georgia and its bigger neighbour are tense. The government in Tbilisi accuses the Kremlin of undermining it.
29 people linked to the pro-Moscow Justice Party were arrested during a series of early morning raids. Its claimed weapons and cash were also seized.
Government officials said Tbilisi would be asking the Kremlin whether it had any connections to the alleged plot, particularly in terms of finance.
In the past, Russia has denied interfering in Georgian politics.
The two countries traded barbs as recently as this week after a helicopter carrying the Georgian defence minister was shot at as it flew over the russian-backed breakaway region of south Ossetia.