Russia and Ukraine say a fight is close.
It would be a big blow to Putin if the city were to be lost.
According to The New York Times, Russian commanders wanted to give it up a month ago.
Russia gave a rare signal of concern as battle looms over one of its important occupied cities.
Russian President Vladimir Putin announced martial law in the region at a high-level meeting in Moscow, while authorities in Kherson were moving people out.
The first Russian city to be invaded was the city. The New York Times reported last month that Putin denied a request from the military to give up the city.
Kirill Stremousov, the deputy head of the occupied government in Kherson, said on Telegram that the battle for the city will start soon.
As of Wednesday, the Ukrainian forces were 19 miles south of the city.
Russia is concerned about how things will go if the city is lost.
The situation in Kherson was not easy and the situation was "tense" according to the new top commander in Ukranian.
The pro-Russia officials left the city on Wednesday as the authorities forced the civilians to leave.
According to The Guardian, a Russian official in Kherson said on Russian TV that between 50,000 and 60,000 people would be taken from occupied Ukranian to Russia.
People lined up for boats over the river.
The four regions of Ukraine that Russia claims to have annexed are Kherson.
The annexations attempt to make them a formal part of Russia are not appreciated by the West.
The city of Kherson has not been made public by the Ukrainian government.
The head of the Ukrainian president's office denied that his country was shelling the city. He said in a Telegram post that the Evacuations were a propaganda show.
Russian terrorists only shoot at Ukrainian cities when planes fall on residential buildings, he said.
Mykhailo Podolyak, a Ukrainian presidential advisor, said on Wednesday that less than a month had passed since Putin's ceremony to recognize the four regions as part of Russia.
He said reality can hurt if you live in a fantasy world.
Business Insider has an article on it.