The cases were confirmed by the Director General of Health, Leausa Dr Take Naseri, the Samoa Observer reports.
A lawyer reportedly told the Supreme Court this week he was unable visit his client at the prison because of restrictions stemming from the measles outbreak.
The Observer was unable to reach the prisons minister for comment.
On Monday, a judge reportedly issued an order restricting the public from entering the courts.
Proceedings continued with journalists able to enter court rooms but members of the public were turned away by police.
