A letter appeared on the Wujie News website earlier this month accusing Xi of a litany of policy mistakes and asking him to step down for the good of the country, before it was deleted.
Media criticism of top leaders is almost unknown in China, where the press is strictly controlled by the ruling Communist Party.
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"I think they are assisting an investigation," said the staffer, adding that the media outlet may be shut down.
A Chinese journalist, Jia Jia, was held last week at Beijing airport while on his way to Hong Kong, with rights groups linking his detention to an attempt to warn Wujie's CEO about the letter.
But his lawyer has said that his detention may not be connected to the document.
Wujie has not published any original articles on its website since Wednesday last week, and has not updated an account on the Wechat social media platform since Friday.
Xi has tightened already strict controls on the media since coming to power in 2012, and recently urged state-run outlets to "reflect the will of the party".
Chinese coverage of Xi is typically limited to accounts of meetings or speeches, or gushing with praise.
He has presided over a slowdown in growth and a clampdown on civil society that has seen hundreds of people arrested.
The letter, seen by AFP in a cached form, berated him for centralising authority, mishandling the economy and tightening ideological controls.
"Due to your gathering of all power into your own hands and making decisions directly, we are now facing unprecedented problems and crises in all political, economic, ideological, and cultural spheres," it said.
Signed "Loyal Communist Party Members" it added: "For the Party cause, for the long-term peace and stability of the country, and for your own personal safety and that of your family, we ask you to resign from all positions of Party and state leadership".
Hong Kong newspaper Apple Daily on Thursday first reported that four staff were missing and added that the outlet was "facing closure".
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