Ms Abbott said Sekone-Fraser has apologised to the New Zealand team and to Papua New Guinea.
"He has withdrawn from the team," she said.
New Zealand athletes at the Pacific Games had to abide by social media policies, Ms Abbott said, as is the case for Olympic Games and Commonwealth games.
News site The Loop PNG captured the images posted on Sekone-Fraser's Instagram account, which has since been deleted.
The first photo was a selfie captioned: "Gearing up for for the opening ceremony #olydix #cannibals #png2015 #weightlifting #pacificgames #papuanewguinea".
The second showed Papua New Guinea dancers in traditional costume and was captioned: "PNG locals getting dressed for town #thepeople #png2015 #pacificgames #stronglikeabull #olydix #cannibals".
The Pacific Games take place every four years. New Zealand has sent a team of 65 athletes including 35 weightlifters, 23 football players and seven taekwondo athletes to this edition of the games.