Six of the nine people confirmed to have the infection in the past month are linked to a person who contracted it at the Green Gathering festival in Chepstow, Monmouthshire.
Since the start of July, measles cases have been confirmed in Swansea, Neath Port Talbot, Pembrokeshire and Powys.
People have been advised to get the MMR vaccine.
All cases have links to festivals in England and Wales and Public Health Wales has warned people they should not attend big events without checking they and their children have had the vaccination.
Measles is a highly contagious viral disease that can cause complications and can even prove fatal.
Measles - what to look for:
An outbreak of measles has been confirmed in Carmarthenshire, Public Health Wales has said.