The company is owned by the son-in-law of former President Eduard Shevardnadze.
"At 6.30 a.m. (0230 GMT) there was an explosion outside the office of Magti mobile company. No one was injured but windows around the office were broken," Tamaz Getia, prosecutor for the region of Tbilisi where the blast occurred, told Reuters.
Shevardnadze quit last month after opposition supporters massed in the capital, Tbilisi, in what they called a "velvet revolution", accusing his allies of cheating them of victory in parliamentary elections.
Georgia was torn apart by civil war after gaining independence from the Soviet Union in 1991.
It has avoided bloodshed since Shevardnadze quit, although there have been a number of blasts in the capital - including an earlier one outside the Magti GSM office four days ago.
Mobile operators are islands of success in the collapsing Georgian economy, which is dominated by shadow trade and plagued by corruption.