The group, which was established in 2011, consists of independent or self-governing countries or territories within the geographical region of Polynesia.
Governor Lolo Matalasi Moliga said because of measles outbreaks in the Pacific, it was prudent to postpone the meeting that was to be held 28-29 January.
In a letter, Lolo said there was "great sensitivity" around the health crisis that might continue into 2020.
The summit is now scheduled for 14-16 April.
The American Samoa leader apologised for the inconvenience but said he was certain everyone shared the same concern for containing the measles outbreak.
The territory was originally set to host the PLG Summit in July 2019 however the governor asked Tuvalu to host it instead.
American Samoa now has 11 confirmed measles cases with one suspected case pending laboratory testing.
So far, more than 13,000 vaccinations have been administered out of a targeted population of just under 16,000.
In neighbouring Samoa, the death toll from the outbreak has reached 83.
Sixteen patients with measles are currently admitted to Samoa's main hospital, including four critically ill children.