Western Sweden has been battling the outbreak since the first case was confirmed on December 10th, and authorities confirmed on Monday the number had risen to 22.
Health officials urged people who do not require medical attention to stay away from hospital premises, to avoid the highly contagious disease spreading further.
“Those who need hospital care should of course come here as normal, but in this situation we want to limit family visits and other visits to hospital,” said Sahlgrenska University Hospital medical director Björn Andersson in a statement.
“Because the infection is spreading we advise against visits to hospital that are not necessary. This is not a visiting ban. If you have to visit a loved one at hospital you may of course do this, but plan your visit with consideration.”
Health officials have previously urged people who believe they are showing symptoms of measles not to come to hospital, but instead call national medical advice hotline 1177.
The first symptoms are high fever, a severe cough and red eyes, followed by a rash.
Sweden has been offering vaccination against measles since 1971 and as part of the MMR jab (measles, mumps and rubella) since 1982.
More than 97 percent of two-year-olds are today vaccinated, however very young children or adults who did not receive the anti-measles vaccine when they were young could be at risk if exposed to the virus.