In a rare show of public dissent, ex-state newspaper editor Li Datong sent an open letter opposing the proposal.
He says in the letter that scrapping term limits for the president and vice-president would sow the seeds of chaos.
China's internet censors have been deleting critical comments across Chinese social media platforms.
There had been widespread speculation that Mr Xi would seek to extend his presidency beyond 2023. The party congress last year saw him cement his status as the most powerful leader since the late Mao Zedong.
State media have been defending the amendment and praising the country's leadership.
China Daily said lifting the term limit was needed "to perfect the party and the state leadership system". The PLA Daily said the move was "very necessary and timely".