Temer himself repeatedly denied any wrongdoing.
A spokeswoman for the Prosecutors Office in Rio de Janeiro told The Associated Press Thursday that Judge Marcelo Breitas had issued the order. Temer's approval ratings were routinely below 10 percent, and he was frequently booed. Temer came to power following Rousseff's impeachment back in 2018 and stayed in office until December 31, 2018.
Local media say police had been trying to trace Mr Temer since Wednesday.
Others who have been arrested so far include former mines and energy minister Moreira Franco who was detained alongside six others.
On leaving office, Mr Temer was asked about potential cases against him but said he was not anxious and did not believe he would be arrested.
Temer took over from Workers Party president, Dilma Rousseff, and was impeached and removed from office in 2016.
Deeply unpopular, the former law professor was replaced in January by far-right President Jair Bolsonaro.
Former Judge Sergio Moro, who oversaw many Car Wash cases and became an internationally known anti-corruption crusader, stepped down at the end of past year to become justice minister.
It started as a federal police investigation into money laundering at a currency exchange business at a petrol station in Brasilia.
Breitas is overseeing the Rio portion of a massive corruption probe involving kickbacks to politicians and public officials.
Operation Car Wash's most high-profile conviction is of former leftist President Luiz Inácio Lula da Silva, who is now serving 12 years in jail for corruption.