Hong Kong has suspended cross-border rail and ferry services, but health workers want a total border closure.
Authorities say closing the border completely would go against advice from the World Health Organization.
There have been 15 confirmed cases of the virus in the city.
"If there is no full border closure, there won't be enough manpower, protective equipment, or isolation rooms, to combat the outbreak," Winnie Yu, chairwoman of the newly-formed Hospital Authority Employees Alliance said.
Hundreds of "non-essential" medical workers went on strike on Monday. The union said frontline workers - including doctors and nurses - would follow on Tuesday if their demands were not met.