The 40-year-old Hero Motorsports rider, taking part in his 13th Dakar Rally since making his debut in 2006, suffered fatal injuries after a fall 276km into Sunday's special stage from Riyadh to Wadi Al Dawasir.
"The organisers received an alert at 10:08 and dispatched a medical helicopter that reached the biker at 10:16 and found him unconscious after going into cardiac arrest," organisers said in a statement.
"Following resuscitation efforts in situ, the competitor was taken by helicopter to Layla Hospital, where he was sadly pronounced dead.
"The entire Dakar caravan would like to extend its sincere condolences to his friends and family."
Goncalves finished in the top 10 at the Dakar Rally four times and was runner-up to Marc Coma in 2015. He was 46th overall after the sixth stage on Friday.
He is the 29th competitor to die at the event and the first since Michal Hernik in 2015.
The Dakar Rally cancelled Monday's stage as a result.
"Paulo, a beloved figure of the rally, was immensely respected by both veterans and less experienced competitors who admired and were inspired by him," a statement read.
"After meeting the riders and making a decision together with the entire motorbike family, the organisers have decided to cancel stage 8 for the motorbikes and quads category, which was supposed to take place on a loop course around Wadi Al-Dawasir, in order to give the riders time to mourn their friend."