The 64-year-old man suffered third-degree burns and remains unconscious in hospital, officials say.
He set himself alight during a protest on Saturday calling for the removal of President Park Geun-hye.
The march in Seoul marks the 11th week of rallies against Ms Park.
The monk, who is being treated at Seoul National University Hospital, left a note urging the authorities to arrest Ms Park for committing “treason” over a reparation deal agreed with Japan in 2015, police said.
South Korea has long called for reparations for the nation’s “comfort women”, who were forced to work in Japanese wartime military brothels.
An agreement was reached between the two nations in 2015 that Japan’s reparations – compensation and an apology – would “finally and irreversibly” resolve the issue.
But critics have said the deal does not go far enough in holding Japan responsible for wartime abuses.
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Tensions between the two countries increased on Friday after Tokyo withdrew its ambassador to South Korea in a row over a statue representing sex slaves.
Japan said the 1.5m-tall (5ft) bronze statue depicting a young, barefoot woman sitting in a chair, was a violation of the 2015 agreement.
On Sunday Prime Minister Shinzo Abe demanded the removal of the statue from outside its consulate in the South Korean city of Busan.
“The South Korean side should show its sincerity,” he said on Japanese TV. He said the 2015 agreement should be implemented regardless of leadership change as a “matter of credibility”.
At the time of the deal, 46 former “comfort women” were still alive in South Korea.
The presidential scandal
In December, Ms Park was forced to step back from her duties after weeks of protests led to her impeachment. But demonstrators are calling for her full removal from office.
The scandal-hit president is accused of allowing a close friend to profit from her parliamentary connections.
The accusations centre on her relationship with a long-time friend, Choi Soon-sil, who faces charges of coercion and abuse of power.
It is alleged that after Ms Park became president in 2013, Ms Choi, 60, used their friendship to pressure companies into donating to foundations she controlled, and then siphoned off funds for her own gain.
Prosecutors are also investigating allegations that Ms Choi sent dubious assets worth hundreds of millions of dollars overseas.
[Source:-BBC]