"Today, at 5:30 in the morning, a car stopped near our building. As soon the car pulled out, an explosion went off," said Gela Daneliya, one of the leaders of the Labor Party.
"Thankfully, nobody was hurt," he added.
The Labour Party does not support Mikhail Saakashvili, who spearheaded the protest that led to Shevardnadze's overthrow.
The bomb attack came days after a bloodless "rose revolution" that saw the overthrow of 75-year-old President Shevardnadze, blamed for plunging the once prosperous Georgia into poverty.
The overthrow, however, was not supported by all of Georgia's political players, and several semi-autonomous regions are also nervous about the outcome of Shevardnadze's fall.
Shalva Natelashvili, the leader of the Labour Party, said the
blast had targeted the party because of its ground support.
"This is a logical extension of Shevardnadze handing over power to his heirs. First, there was serious pressure against the government channel" and other independent media, he said. "And now they have got to us."
Natelashvili added: "This is happening because of our high
Shevardnadze, a former Soviet foreign minister credited with having helped end the Cold War, was forced from office last Sunday after weeks of angry protests against alleged fraud in 2 November parliamentary elections which returned his government to power.