On YouTube, the video of the 20-minute segment was viewed more than 3.3 million times by Friday.
The show also turned a critical eye to Xi's signature anti-corruption crackdown that has ensnared political rivals and his hallmark programme of overseas infrastructure projects known as the "Belt and Road" initiative.
Oliver's show included a parody of a propaganda music video made to promote the initiative in which children sing about China being an autocracy that abuses its citizens' human rights.
"This is the China Xi doesn't want you to see," they sing in chorus.
It also discussed moves to build up a cult of personality around Xi, the ruling Communist Party's attacks on human rights campaigners and the death of Nobel Peace Prize laureate Liu Xiaobo last year while serving a prison term for subversion.
The censoring of social media posts was the latest sign of the country's increasing sensitivity over political content and satire.
China maintains some of the world's toughest restrictions on content online as well as on foreign news and entertainment broadcasters such as HBO.
Weibo did not immediately respond Friday to a request for comment.
- AP