The wife of the opposition Democratic Party leader, Serdar Calaloglu, said men wearing masks had kicked down the door of their apartment and dragged him away.
The OSCE democracy watchdog criticised Wednesday's vote, citing cases of ballot-stuffing, intimidation of the opposition and police violence. The opposition claims it was robbed of victory.
The newly elected president, Ilham Aliyev, promised on Saturday he would not stand for a repeat of riots the day after the poll when, an official in his party said, two people were killed in clashes between protesters and truncheon-wielding police.
He accused Musavat Party leader Isa Gambar, runner-up in the election, of being behind the riots, in which about 3000 protesters hurled stones, overturned cars and fought police.
“I see the mass unrest as an attempt to push the country back to the early 1990s by the same people who provoked the trouble then ... These people want to bring in chaos, but this will not happen”
President Ilham Aliyev
“Isa Gambar should expect the judgment of the Azeri people as a provocateur and a person who has blood on his hands,” Aliyev said at an Independence Day ceremony.
Gambar, who as a presidential candidate enjoys immunity until official results are announced, was defiant in an interview at his Baku flat, which he said was under police surveillance. Three foreign observers were staying with him.
“No threats will intimidate me and my comrades-in-arms. We will continue peaceful struggle for democracy in accordance with the constitution of Azerbaijan,” he told Reuters. Gambar dismissed suggestions he may ask for political asylum abroad.
Thursday's violence highlighted animosity towards the new president, who took over from his sick father, Haydar Aliyev, in the first dynastic succession of the ex-Soviet world.
Azerbaijan's leaders have long been criticised by human rights groups, but have often received support from Western governments and investors, including BP, which has an interest in seeing the completion of an oil pipeline being built between Baku and the Mediterranean Sea.
“I see the mass unrest as an attempt to push the country back to the early 1990s by the same people who provoked the trouble then ... These people want to bring in chaos, but this will not happen,” Ilham Aliyev said.
Interior Minister, Ramil Usubov, said about 200 people had been detained after Thursday's violence. Independent reports say some of them have already been given short prison sentences.
Usubov also reported 50 policemen and 16 soldiers were injured in Thursday's protest, 20 seriously. One officer received stab wounds and one civilian died. Rights groups said a total of 300 were injured.