There were no casualties reported in the incidents.
Ground traffic in the province of Adjara, a key oil link to the Black Sea, mainly goes to the rest of Georgia over a bridge on the Choloki river.
"We are taking preventive measures," the regions separatist leader Aslan Abashidze told reporters.
"The situation is explosive -- it is prompted by the Georgian president's decisions to establish a dictatorship over Adjara," said the interior minister of Adjara, Dzhemal Gogotidze.
The decision to blow up the bridges was a "preventive measure," he said, adding that Adjara would continue to press for the withdrawal of Georgian troops from its borders.
The incidents marked a new escalation of tensions between the former Soviet republic's young President Mikhail Saakashvili -- a pro-Western leader -- and Adjaran chief Aslan Abashidze, who has close links to Russia.
The top Russian foreign ministry spokesman, Alexander Yakovenko, told Moscow Echo radio that a Georgian invasion of the region would have "catastrophic effect".
The blasts came as Saakashvili, 36, traveled to the Georgian port town of Poti, where he boarded a warship to oversee the naval exercises on the shores of Adjara.
"I would suggest to Aslan Abashidze that he does not provoke the situation further," Interfax quoted Saakashvili as saying on board the ship Sunday.
"How long can they really keep this border closed?" he later asked in remarks broadcast on television.
But he added: "We do not plan to stage a military operation in Adjara."
Still, Saakashvili cut short his trip on board the warship and rushed off to Poti for military consultations after hearing of the bridges' ruin, officials told AFP.
Meanwhile a Georgian group called Nasha Adjara (Our Adjara) said they were planning Sunday to stage a mass meeting before the ruined bridge Sunday, the same site where the Georgian president was recently turned away by local Adjaran militia.
Tensions between Tbilisi and Adjara escalated this week as Abashidze ordered preparations for a military mobilization in Adjara and Saakashvili warned he would use force to bring the renegade region in line.
Saakashvili said Georgia's forces -- which launched their exercises Friday and once imposed a brief economic blockage on the region -- would "take care of" Abashidze should he fail to back down in the escalating confrontation.