"Movement has been closed for civilians and their vehicles. But the ban does not affect employees of international organizations or peacekeepers based in the security zone of the Georgian-Abkhazian conflict," a Georgian police source said.
He said there had been no incidents along the separation line.
Abkhazia announced the border closure after two bombs exploded Monday at a market in its capital Sukhumi. Earlier reports that one person had been killed were unconfirmed.
On Sunday, six people were injured when two explosions rocked Abkhazia's Black Sea resort of Gagra.
Abkhaz President Sergei Bagapsh blamed Georgia for the bombings.
Tbilisi called the accusations "absurd."
Abkhazia broke away from Georgia in the early 1990s following the collapse of the Soviet Union. Between 10,000 and 30,000 people were killed in the subsequent fighting.
The pro-Western Georgian government of Mikheil Saakashvili has said it is determined to bring the breakaway region back under its control.
