Sources told BBC Arabic that more than 100 hundred people gathered outside the police department in capital Riyadh in anger at Ali Jabiri Alhouraysi’s death.
He is said to have killed himself after being searched by police.
The incident echoes the death of a Tunisian who set fire to himself as a protest in 2011, triggering revolution.
The death of Tunisian vegetable seller Muhammad Bouazizi helped spark protests that led to the toppling of Tunisian President Zine al-Abdine Ben Ali a week later, and is considered as one of the catalysts for the regional Arab Spring.
Like Mr Bouazizi, Mr Alhouraysi was a vegetable seller.
The BBC understands Mr Alhouraysi killed himself on Wednesday after being unable to present his identification papers when he was searched by police. He is said to have been previously stripped of his Saudi citizenship.
The sources told BBC Arabic that Mr Alhouraysi’s family is refusing to receive his body from the hospital.
Reports of self-immolation in the ultra-conservative kingdom are rare. Two years ago a man in his 60s has died after setting himself on fire in Samitah in Saudi Arabia’s south-western Jizan region.
Unconfirmed reports say he was angry about the difficulties in obtaining citizenship.
Saudi Arabia has largely escaped the unrest that has affected some countries in the region, although it has faced low-level protests in its Eastern Province, where most of its Shia Muslim minority live.