The explosion rocked the parliament building just as Mr Shevardnadze was leaving. Tass news agency suggested the bomb was planted in a car parked near the building.
Television film showed Mr Shevardnadze sitting in a chair looking dazed shortly after the explosion. His face and hands were bloodied, apparently from flying glass. He was later taken to hospital.
Mr Shevardnadze said the attempt had been "engineered by destructive forces seeking to destabilise the situation in my country". He had been "targeted personally". Tass quoted witnesses as saying that several cars were destroyed in the garage beside the parliament. Six other people were said to have been wounded.
Power struggles in Georgia have been frequent and violent in the past few years. The list of potential assassins is long. Elections are due to held later this year.
In December 1991, as the Soviet Union was officially wound up, armed rebels overthrew the then president, Zviad Gamsakhurdia, in a brief but bloody civil war. Mr Shevardnadze, famous as the Soviet foreign minister, became leader and was confirmed in elections at the end of 1992.
The following year, Mr Gamsakhurdia launched an armed rebellion from his stronghold in western Georgia, which failed. Mr Shevardnadze, meanwhile, remained at odds with some of the leading members of his own government.
Jaba Ioseliani, who had served a prison sentence for bank robbery, was in charge of an armed militia known as the Mkhedrioni (Horsemen). Mr Shevardnadze recently disarmed them
The Georgian leader also angered nationalists by apparently deciding to return to Moscow's fold.
He signed up for the Commonwealth of Independent States, which Georgia had originally ignored.
Then, earlier this year he signed an agreement which allows Moscow to shore up its military presence in Georgia.
Mr Shevardnadze visited Britain earlier this year in an attempt to advance Georgia's prospects. That such assassination attempts can take place will remind would-be investors that the region is still far from calm. A crucial oil pipeline, which would give Georgia international clout, might now be routed via the Russian Black Sea port of Novorossiisk.
Another persistent source of instability has been in the breakaway region of Abkhazia. Georgians have fled from areas controlled by the Abkhazians and Abkhazians have fled from the Georgians.
The Russians have been present in the region as an alleged peace-keeping force, although many observers believe Moscow has clearly taken the side of the Abkhazians.