Ukrainian authorities have urged residents to leave Kherson due to the threat of a "harsh winter".
Queues have formed on the outskirts of the city as hundreds of civilians try to escape Russian attacks.
Kherson was recaptured by Ukraine on November 9, which was celebrated by residents in the streets and squares with jubilation and singing the national anthem.
But in recent days, the city has been hit hard by bot attacks.
- There is no other option but to leave.
I see no other way out.
Three to four days after Russia left Kherson, heavy shelling began.
Many people died and were injured.
Russia is shooting at the center, homes, everything, says Sergey Semeyko, a resident of Kherson, to the AP news agency.
At least 32 civilians dead
Many are also trying to leave the city by train to Khmelnytskyi, where, according to Ukrainian authorities, they will receive financial support, housing and humanitarian aid.
Others are evacuated via bus to Mykolajiv and Odessa, where they are temporarily allowed to live in specially equipped shelters before they can move on to safer cities, writes CNN.
On Thursday, the region's governor, Yaroslav Janusevytj, wrote on the messaging app Telegram that the city had been shelled 49 times and that robots, among other things, had struck a residential area.
At least 32 civilians have died as a result of Russian attacks in Kherson since the city was liberated, Ukraine's national police chief Ihor Klymenko said, Reuters reports.