Mr Temer, a 78-year-old lawyer who was in office from 2016 to 2018, is being investigated in several cases.
He has consistently denied any wrongdoing. His arrest was considered imminent after he lost his legal protection when he left office.
Many politicians and business leaders have been convicted or charged as part of the so-called Operation Car Wash.
Mr Temer was arrested in his hometown of São Paulo on Thursday morning local time and will be flown to Rio de Janeiro.
Local media say police had been trying to trace Mr Temer since Wednesday. His former Mining and Energy Minister Moreira Franco was also arrested.
Who is Michel Temer?
Mr Temer, from the centre-right MDB party, took over the Brazilian presidency in August 2016 following the impeachment of leftist Dilma Rousseff, a process in which he played a key role.
While in office, Mr Temer was hit by corruption charges which were blocked by his allies in Congress.
Deeply unpopular, the former law professor was replaced in January by far-right President Jair Bolsonaro.
What is Operation Car Wash?
"The largest foreign bribery case in history", as it was dubbed by the US Department of Justice, began in March 2014.
It started as a federal police investigation into money laundering at a currency exchange business at a petrol station in Brasilia.
The probe widened and looked into allegations that executives at the state oil company Petrobras had accepted bribes from construction firms in return for awarding them contracts at inflated prices.
The corruption scandal involves millions of dollars in kickbacks and more than 80 politicians and members of the business elite. It provoked huge street protests nationwide.
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.