Some residents told The New York Times they were concerned Ukrainian troops would invade Russia.
In recent weeks, Ukraine has regained thousands of square miles of its territory from Russia.
Another resident said "rumors" were swirling of Ukrainian troops crossing the border for the first time during the war.
"There are so many rumors, people are afraid," Maksim, who sells military and outdoor gear at the market, told The Times.
"We feel scared, and it is especially hard when you work with children," Ekaterina, a kindergarten teacher, told The Times.