Indonesian police confirmed the death toll based on reports from hospitals. They said the cause of the deaths was being investigated.
The national police chief has denied his officers used live ammunition.
Police fired tear gas at protesters when clashes broke out again in the capital on Wednesday.
Protesters hurled fireworks and rocks at police during a stand-off near the election supervisory agency, while clashes also restarted in other areas of the city.
Social media has been restricted in some areas to stop rumours spreading.
The protests erupted after official election results showed Mr Widodo had beaten his long-time rival Prabowo Subianto at the polls last month.
How have the authorities responded?
National police chief Tito Karnavian said some of the six dead appeared to have gunshot wounds and others “blunt force wounds”.
The authorities have said the protests were planned and “not spontaneous”. They have suggested that a group of provocateurs may have been responsible for the violence.
“A majority of the protesters came from outside of Jakarta,” said Muhammed Iqbal, a police spokesman.
President Widodo has promised firm action against rioters.
“I open myself to anyone to work together to build and develop this nation, but I won’t tolerate anyone who tries to disrupt public security, the democratic process or the unity of our… country,” the president said at a press briefing.
How did the protests start?
Protests in the capital Jakarta began peacefully on Tuesday but soon turned violent, with cars set on fire and firecrackers thrown at police.
Police in riot gear fired tear gas to disperse the crowd.
The country’s General Election Commission confirmed on Tuesday that Mr Widodo had won the presidency, taking 55.5% of votes.
Mr Prabowo rejected the results, alleging cheating, but the election commission dismissed his claims.
The ex-general also lost against Mr Widodo at the last election in 2014, and went on to unsuccessfully challenge the results.
More than 192 million people were eligible to vote in the presidential and general elections that took place on 17 April.
After the official results were announced on Tuesday, thousands gathered in front of the election supervisory building in support of Mr Prabowo, but later moved on to other areas across Jakarta after police urged the crowd to disperse, according to BBC Indonesian.
Local TV stations showed several standoffs between protesters and police in parts of the city.
More than 30,000 troops had been deployed in Jakarta in anticipation of potential violence.
Mr Prabowo repeated calls for supporters to protest peacefully.
“We support people’s constitutional rights [to protest] as long as they are civilised, peaceful and non-violent,” he told reporters.
On Wednesday, chief security minister Wiranto, who uses just a single name, said access to social media would be blocked in some areas.
The restrictions – including on photo and video sharing – aimed to control the spread of misinformation, he said.