Faris Maumoon, a Member of Parliament and son of former president Maumoon Abdul Gayoom, was taken into custody after police searched his home in the capital, Male, on Tuesday.
The passport of another key opposition figure, Qasim Ibrahim, a former ally of strongman Yameen, was also seized by authorities.
Opposition parties aligned against President Yameen issued a joint statement condemning the arrests.
Ibrahim had helped Yameen win a controversial 2013 run-off election against Mohamed Nasheed, the head of the main opposition Maldivian Democratic Party.
But after a fallout, Ibrahim joined the growing ranks unifying behind Nasheed and the MDP to topple Yameen.
The opposition this month secured enough support from government defectors to begin impeachment proceedings against the Speaker, in a bid to wrest control of parliament from Yameen before presidential elections next year.
The latest arrests come a week before parliament is due to vote on the impeachment proceedings.
“The opposition fears the imminent arrest of more members of parliament who signed the impeachment motion,” the opposition said in its statement.
The first attempt to impeach the Speaker sparked chaos when Yameen ordered troops to enter parliament and remove dissenting opponents by force.
That move attracted international condemnation, with the United States urging the Maldives to restore faith in democracy.
The political unrest has raised fears over stability in the islands and tarnished its image as a tourist paradise.
Nasheed became the Maldives’ first democratically-elected president in 2008, but he was narrowly defeated by Yameen five years later in a controversial run-off election.
In 2015, Nasheed was sentenced to 13 years in prison on terrorism charges that were widely seen as politically motivated.
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