"We can confirm that (Cunha) was detained in Brasilia," a police spokesman told AFP.
G1 news site published a copy of the arrest warrant issued by the office of top Brazilian anti-corruption judge, Sergio Moro.
Cunha, nicknamed Brazil's Frank Underwood after the scheming main character in the dark US political series "House of Cards," initiated the impeachment process that finally forced Rousseff out of office this August.
The leftist president was found guilty of fiddling government accounts. However, she accused Cunha, from the conservative evangelical movement, of mounting a coup.
Cunha's downfall signals that the Petrobras corruption probe headed by Moro is continuing to send shockwaves through Brazilian politics.
Dozens of politicians and executives have already been charged or convicted with involvement in the embezzlement and bribery scheme.
Rousseff's presidential predecessor and leftist icon Luiz Inacio Lula da Silva faces three corruption-related court cases and speculation is rife that he could also be place in pre-trial detention.
Several of his choices for ministerial posts have been accused of taking part in the embezzlement.
Temer says the Petrobras inquiry, dubbed Operation Car Wash, should continue.
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