The party said Serhiy Yevtushenko was detained yesterday, immediately after arriving in Baku with a Ukrainian delegation.
He had been invited by Azerbaijan's Musavat opposition party. Pora began as a pro-democracy youth movement and played a key role in last year's Orange Revolution in Ukraine.
The group has since been registered as a political party. The international community has long pressed the government of Azerbaijani President Ilham Aliyev to improve its democratic credentials and ensure that legislative polls due later this year are free and fair.
[For more on events in Azerbaijan and that country's looming elections, click here.]