Opposition supporters in Port Gentil, Gabon's second-largest city, set fire to France's consulate general after Bongo's victory was announced, witnesses said.
Prisoners who had been set free or escaped from a local jail were roaming the streets and set fire to a petrol station, a resident told French state radio France Info.
"There are thousands of people. There is the opposition, but it is not just the opposition," he said.
"Everyone is taking advantage of this, not just the prisoners."
Al Jazeera’s Mohamed Adow, reporting from Libreville, said: "The post election unrest in Gabon is spreading and it is spreading very fast.
"Supporters of the opposition took to the streets and they invaded a prison and released hundreds of inmates.
"The French government is being accused of standing right by Ali Bongo."
Tear gas fired
About 10,000 French citizens living in the country were warned by French officials to stay indoors after the rioting broke out.
"Measures are in place to ensure the security of French citizens," Alain Joyandet, the international development minister, told the Agence France-Presse news agency.
"We have taken measures to keep them in, it is recommended to French people to stay at home."
Security forces had earlier used tear gas to disperse hundreds of opposition supporters who had led an overnight sit-in on a square near the election commission in the capital.
Officials said on Thursday that Bongo had won the election with just over 40 per cent of the vote.
Tight rule
Ex-defence minister Bongo, 50, scored 41.73 per cent of the vote, the interior ministry announced, ahead of ex-interior minister Andre Mba Obame and Pierre Mamboundou, who were nearly tied, receiving 25.8 and 25.2 per cent of the vote respectively.
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| Officials said that Bongo had won the poll with 41.73 per cent of the vote [AFP] |
Just over 800,000 voters registered to take part in Sunday's election.
The poll was called after Omar Bongo's death in June, ending nearly 42 years of his tight rule over the central African oil nation.
Adow said that "police have been dealing with the protesters heavy handedly".
"Obamer and Mamboundou said the elections were fraudulent right from the beginning.
"They say they will not accept the results and have called upon their supporters once again not to support the election results."
Results questioned
Ali Bongo's rivals had said they feared the official results were being massaged to ensure a dynastic succession from father to son, an accusation Bongo has denied.
Observers and financial markets have played down the risk of major instability in the tiny country, but some unrest was expected given the dispute over the result.
The death of 73-year-old Omar Bongo ended a period that brought his country stability.
Gabon hosts oil firms including France's Total and US-based Vaalco, and is one of the few sub-Saharan countries to have launched a the international bond Eurobond.
Analysts say Ali Bongo now faces the challenge of diversifying the economy to replace revenue from Gabon's dwindling oil reserves.