The government said the latest case was a 28-year-old man from Fagaitua village, who has not left American Samoa in the past three months.
A woman, 27, is also thought to have measles, with samples sent to Hawaii for testing.
The territory is under an emergency declaration, with travel restrictions imposed on the territory's border, public gatherings restricted, and a mass vaccination campaign underway.
Earlier this week, the US announced it would provide $US490,000 of funding to help support the territory's efforts to prevent the spread of the virus.
An epidemic in neighbouring Samoa has claimed the lives of 83 people and infected thousands in the past three months.