Sunday's protest had taken place in Bern's centre and was scheduled by police to end at noon, before Mr Xi's visit.
City authorities said the demonstration mostly proceeded peacefully but a number of participants had continued to protest past the deadline, refused identity checks, and caused other disruptions.
Police spokesman Christoph Gnaegi told the Associated Press that those arrested were later released.
Doctors had taken care of the man who had tried to set himself on fire.
The demonstration attracted between 700 and 800 protesters, organisers said.

China's policies in Tibet have frequently prompted overseas protests by Tibetans calling for freedom from China and acceptance of their spiritual leader-in-exile the Dalai Lama.
In 1999, a similar pro-Tibet protest took place during a visit by China's then-president Jiang Zemin, who was said to be angered when demonstrators threw eggs at the Chinese delegation.