The Swedish news agency Tidningarnas Telegrambyra reported Tuesday that Jonsson was detained along with two other "top level colleagues."
The three were held for questioning in separate rooms "because the risk is that they get together to sync their stories," said financial prosecutor Olof Sahlgren.
Suspicion centers on taxable income earned in 2010-11, the period in which Saab executives scrambled to find funding to revitalize the brand.
The company was declared bankrupt in December 2011.
Jonsson, who joined Saab in the 1970s and worked for the company in Asia, the United States and Europe, was named CEO in 2005, just as the toughest years began.
By 2010, the company's owner, General Motors, was unwinding the brand. It was bought that year by Dutch firm Spyker Cars, and the effort to find additional funding continued and ultimately came up short.
Jonsson left the company in March 2011, citing personal reasons.
He faces a possible four-year jail term if convicted, the news agency said.