All the cases were discovered in adults. Two of the cases may be related, with a colleague turning into the hospital after contact with the 'patient zero'.
Another of the patients had been travelling abroad, so it is unclear whether he was infected in Latvia, while the fourth caught the disease locally.
All of them are currently being treated at a hospital.
None of them were children, which means that vaccine coverage is good among the younger population, said Latvia's Center for Disease Control and Prevention.
By December last year, Latvia and Malta were the only EU countries that had been measles-free for the previous twelve months.