Diego Dzodan, an Argentine national, has repeatedly refused to comply with court orders to hand over data for use in a criminal investigation into drugs trafficking, police said.
His arrest relates to the messaging service WhatsApp, owned by Facebook.
In a statement, Facebook called Diego Dzodan’s arrest an “extreme and disproportionate measure”.
Diego Dzodan’s arrest was ordered by a judge in the north-eastern state of Sergipe.
He was held as he left his house in an exclusive area of Sao Paulo on March 1.
Judge Marcel Maia Montalvao had in two previous instances issued fines against Facebook for refusing to release WhatsApp data.
The information was needed as part “secrete judicial investigations involving organized crime and drug trafficking,” he said.
In a statement, Facebook said it was “disappointed with the extreme and disproportionate measure”.
“Facebook has always been and will be available to address any questions Brazilian authorities may have,” the company said.
In December a judge in Brazil suspended WhatsApp for 48 hours.
The Sao Paulo state judge said at the time that WhatsApp failed to comply with court orders to share information in a criminal case.
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