New figures show there are now 316 cases in the city — with 64 new cases reported in the last week alone.
Public health experts said the disease had now spread to youngsters in 111 secondary and primary schools, nurseries and playgroups.
It means that children who haven't had the jab have an increased risk of coming into contact with those already with the highly contagious virus.
The majority of cases were in Swansea, but cases have also been reported in the Mid and West Wales region.
Dr Marion Lyons, director of health protection for Public Health Wales, said: "Measles is such an infectious disease that around 90 per cent of unvaccinated people who come into contact with cases will catch it. You only need one or two people who haven't had the vaccination to put at risk babies, toddlers and anyone else who is vulnerable, such as children with leukaemia who cannot have the vaccination and pregnant women who haven't been vaccinated.
"We cannot emphasise enough that measles is an illness that can kill, or leave people with permanent complications including severe brain damage.
"The only protection is the safe and highly effective MMR vaccine."
