Reporters say Port Gentil's main market was also set alight, but government and French buildings were not targeted.
Before the curfew, opposition supporters had set fire to the French consulate in the city, accusing France of helping to rig the election.
The poll came after the death of Ali's father, who had ruled for 41 years.
Under Omar Bongo, Gabon retained close ties to the former colonial power.
The AFP news agency reports that 50 people were arrested on Thursday night during the unrest.
After the results were declared on Thursday, opposition groups clashed with security forces in the capital, Libreville.
Inmates were freed from jail and installations belonging to the French oil company, Total, were attacked in Port Gentil.
France has about 1,000 troops in the country and has advised its 10,000 citizens to stay indoors.
The BBC's Linel Kwatsi in Libreville says the situation in both cities is now calm.
Amid the unrest, pledged to be a uniting force for the oil-rich nation.
He was widely tipped to succeed his father, who died in June.
One of the world's richest men, the late president owned a string of properties in France and was an unflinching ally of Paris.
At the time of his death, French courts were investigating Mr Bongo for corruption - allegations he denied.
Gabon is sub-Saharan Africa's fourth biggest oil producer and Africa's second biggest wood exporter, although most of its 1.4 million people live in poverty.