The arrest came after police rescued Aparecida Schunck Flosi Palmeira, the 67-year-old mother of Ecclestone's Brazilian wife, Fabiana Flosi, on Sunday night after more than a week in captivity.
The pilot, Jorge Eurico da Silva Faria, "planned the kidnapping and knew these people's routines," said the Sao Paulo state security service.
It said the pilot worked for Ecclestone's family. Brazilian news reports said he had also worked for Ecclestone personally.
Schunck, who was kidnapped on July 22, was rescued by the police in a massive night-time raid in the city of Cotia, in the greater Sao Paulo area.
Two suspects were immediately arrested at the scene on Sunday.
Schunck was unharmed but shaken after more than a week in captivity.
She spoke briefly to television cameras as she arrived at a police station after being freed, before hugging waiting relatives.
"No one should kidnap anyone in Sao Paulo because they will get arrested," she said, her voice breaking with emotion.
A demand for a ransom of $36.6 million was made to the family, according to weekly news magazine Veja.
But no ransom was paid, according to the governor and police sources.
Kidnappers posing as delivery men abducted Schunck from her home in the Jardin Santa Helena area of Sao Paulo, neighbors told AFP last week.
A police source said investigators managed to identify the abductors' car on security camera footage and trace it to the house where she was held.
Schunck's home is in the southern Interlagos neighborhood, which hosts the Brazilian circuit of the F1 Grand Prix.
Before her daughter married Ecclestone, she lived in the impoverished neighborhood of Santa Francisca Cabrini.
Flosi, a 38-year-old Brazilian lawyer, met the 85-year-old Ecclestone while she was working for the Interlagos Grand Prix in 2009. The couple married in Switzerland and now live in London.
Schunck's kidnappers struck just days before Brazil hosts South America's first Olympic Games from August 5 to 21.
Foreign athletes, media and visitors have reported thefts and robberies in the crime-plagued host city, Rio de Janeiro, which is an hour's flight northeast of Sao Paulo.
Kidnappings were common in Brazil in the late 1990s and the early 2000s, but dropped with more intensive policing and creation of a specialised anti-kidnapping department.
Relatives of footballers were particularly targeted, including the mother of Brazilian national team star Robinho in 2004. She was held for 41 days on the outskirts of Sao Paulo.
There were reports that she was freed after payment of a ransom of up to $200 000, although the footballer never confirmed this.
Another high-profile case involved the father of football star Romario in 1994. He was held for seven days before being freed. More recently, the sister of national team player Hulk was held for 24 hours in the state of Paraiba.