The opposition leaders also announced they were creating a transitional council, and have said Ouattara is violating the constitution by seeking a third term.
Ouattara has said the approval of a new constitution in 2016 restarted his mandate and allowed him to run again.
N'Guessan served as prime minister from 2000-2003 under President Laurent Gbagbo.
In 2010 Gbagbo refused to concede defeat to Ouattara, leading to a civil war that killed about 3,000 people.
More than 40 people have died in clashes in the country, which is the world's leading exporter of cacao, since August.
Ivorian police have not publicly confirmed N'Guessan's arrest, but both N'Guessan's wife and a publicist have told reporters he was detained Friday.