Correio da Manhã and Público have confirmed the detention of Ecclestone on Monday morning.
The 95-year-old businessman is in the custody of the Public Security Police following a routine operation on the aircraft he was travelling in.
During the procedure, a shotgun was found in Ecclestone's possession. There has not yet been any official announcement.
One of the most prominent figures in Formula 1, where he arrived in the 1950s, Ecclestone helped negotiate commercial partnerships, sponsorships, television rights and contracts with circuits.
He stepped away in 2017, when Liberty Media acquired the commercial rights to the premier competition.
He owns a mansion in Quinta da Marinha, purchased for around 40 million euros.