The opposition party Wefaq said the body of Salah Abbas Habib, who was 37, was found on the roof of a building in a rural village.
They claim the man was part of a group who were beaten by police.
Wefaq, the leading party among Bahrain's Shi'ite Muslim majority population, published a photograph taken of Habib's body.
Bahrain's Interior Ministry said via Twitter that it was launching an investigation.
Armoured vehicles and security forces in riot gear were deployed along the road to the Bahrain International Circuit and around the capital, Manama. Activists said barbed wire has been installed near some parts of the main highway.
The protesters, mostly from the majority Shi'ite Muslim community, blame the Sunni ruling elite for shutting them out of opportunities, jobs and housing.
They have made it clear they will use the international attention the motor race has focused on Bahrain to air their grievances.
There were no protesters near the Grand Prix circuit, which was blanketed with layers of security. Saturday's practice runs began without incident.
Organisers have rejected calls from human rights groups to cancel Sunday's race because of what activists see as continuing political repression.
Around 5,000 people marched through Manama to express their dissatisfaction at the presence of the sport in the country at this time.
But, speaking to the BBC, Formula One chief executive Bernie Ecclestone said:
It was reported that following the march protesters clashed with police. It is understood that Bahraini police fired tear gas to break up a protest in a Shi'ite district outside Manama and protesters responded with petrol bombs.
A witness told the news agency Reuters there were up to 150 protesters, who had taken part in a march of several thousand earlier for democratic reforms and against Formula One, and around 50 riot policemen in jeeps.
Labour leader Ed Miliband added his voice today to demands for the race to be called off, urging the Prime Minister to do the same.
William Hague spoke to his counterpart in Bahrain, calling for restraint.