His body was found in the Shia village of Shakhoura, near the capital, Manama, an opposition group said.
On Friday, tens of thousands took part in at times violent protests demanding an end to the crackdown on dissent in the run-up to the rally.
Armoured vehicles are patrolling the streets of Manama ahead of the race.
The discovery came as practice and qualifying sessions for the Grand Prix were taking place. Mainly Shia protesters have announced “days of rage” against the race.
Formula 1’s governing body, the FIA, only went ahead with the Grand Prix after the government said it had security under control.
Last year’s Grand Prix was cancelled after 35 people died in February and March during a crackdown on mass demonstrations calling for greater democracy.
The protesters demand an end to discrimination against the majority Shia Muslim community by the Wahabi royal family.
Human rights groups and activists estimate that at least 85 people have died since the start of the protests, many as a result of what has been described as the excessive use of tear gas.
Activists from opposition group al-Wefaq said the man found dead on Saturday, variously named as Salah Abbas Habib or Salah al-Gattan, 37, was killed by government forces.
Several others were hit by birdshot in the incident, Nabeel Rajab from the Centre for Human Rights told the BBC.
In a message posted on Twitter, the Bahraini Interior Ministry confirmed that a dead person was found in Shakhoura. It said police had launched an investigation.
On Friday, Bahrain’s Crown Prince, Salman bin Hamad Al Khalifa, said cancelling the Grand Prix “just empowers extremists”, and insisted that holding the race would “build bridges across communities”.
Jean Todt, the president of the motor racing governing body, the FIA, said he had no regrets about the race, as extensive investigations into the situation in Bahrain had unearthed “nothing (that) could allow us to stop the race”.
“On rational facts, it was decided there was no reason to change our mind,” Mr Todt said.
The Shia protesters say going ahead the race lends international legitimacy to a government that is continuing to suppress opposition with violent means.
Al-Wefaq said security forces had beaten protesters in Shakhoura with tools and weapons, according to the AFT news agency.
The group reported on Saturday that 70 people had been injured by security forces in the past two days and 80 others arrested.
Meanwhile, the daughter of political and human rights activist Abdul al-Khawaja, who has been on hunger strike for more than two months, was briefly detained when she went to see him in hospital, Nabeel Rajab said. She was not allowed to see her father.
Mr Khawaja launched his hunger strike in protest against a life sentence handed down by a military tribunal in June.
He stopped drinking water on Thursday, according to his daughter, Zainab.
She told the BBC that on Saturday her father was in a critical state.
“He’s on the 73rd day of his hunger strike and the last call he made yesterday, he asked for his lawyer to go see him so he could write his will.
“We’re afraid that we might never hear of him again, and that we might not see him again.”
During Friday’s protests, tens of thousands people walked along a motorway from Budaiya, an area to the west of the capital, Manama.
Police fired stun grenades and tear gas at a small group who tried to reach the site of the former Pearl Roundabout, which was at the heart of the initial mass anti-government protests last year.
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