Shota Utiashvili, an interior ministry spokesman, said the mutiny ended without violence.
"It's over. Most of the people have surrendered. A few people have escaped," he told the AFP news agency.
Matthew Collin, Al Jazeera's correspondent in Tbilisi, said: "Saakashvili has visited the area which is a sign that the incident is back under control. We still don't know how many people took part in the events.
"The growing instability in the region will not help Georgia's Nato application".
David Sikharulidze, the country's defence minister, had said the rebellion was aimed at disrupting Nato exercises which are due to be held in Georgia from Wednesday.
Saakashvili suggested Russia was behind the mutiny, saying those involved had "connections with special forces in a specific country known to us".
"I am asking and demanding from our northern neighbour to refrain from provocations," he said.
But Moscow's envoy to Nato denied any involvement in the mutiny, saying Saakashvili was attempting to distract attention from domestic problems.
|Mikheil Saakashvili suggested Russia was behind Tuesday's rebellion [AFP]
"The fact that a mutiny broke out at a Georgian defence ministry brigade is just a reflection of the all-embracing political and economic crisis that is developing under Mikheil Saakashvili's presidency," Dmitry Rogozin told the Reuters news agency.
"Saakashvili and his entourage are trying to explain the consequences of their foolishness by [accusations of] Moscow's underhand plotting."
Neave Barker, Al Jazeera's correspondent in Moscow, said: "Russia has decribed the allegations as a complete provocation."
Barker quoted Rogozin as saying that going ahead with the Nato exercises in Georgia would be "like holding exercises in an asylum".
Earlier, a Georgian interior ministry spokesman said they had uncovered a Russian-backed plot to overthrow the government, organised by a former special forces commander.
Utiashvili said the "rebels were in direct contact with Russians" and were receiving orders and money from them.
He said the organisers of the plot were former high-ranking defence ministry officials, and that at least one had been arrested.
Collin said it was unclear how serious the mutiny was, but it was "clearly bad news for Mikheil Saakashvili," who has been facing demonstrations in the capital over the last few weeks demanding his resignation.
He said it was not clear whether the rebellion would affect the upcoming Nato exercises, which will be taking place at a "very different military base".