This latest rankings are to be used for the draw for the 2018 World Cup. The men's national team was ranked 69th in November 2014.
Greece and Sweden are the other unseeded teams for the draw, which is live on Sky Sports News from 1pm on Tuesday.
The current frontrunners in FIFA's top-ten rankings are reigning World Champions Germany (1,631 points), followed by Brazil (1,619), Portugal (1,446), Argentina (1,445), Belgium (1,333), Poland (1,323), France (1,226), Spain (1,218), Chile (1,173) and Peru (1,160).
What are Northern Ireland and the Republic's play-off records?
The eight teams qualified for the play-offs are will be divided into two pots.More news: Soccer star George Weah leading Liberia elections
Who will be the team for Northern Ireland and the Republic to avoid? They may be lower than Switzerland in FIFA's rankings, but they will still be a formidable opponent. Once one ball has been taken from pot one and another from pot two, they will be placed in a central pot, mixed and then drawn one by one. The team drawn first will be at home in the first leg.
When and where does the draw take place?
Four two-legged ties will be played, with the first leg taking place between 9 and 11 November and the return between 12 and 14 of the same month.
New Zealand have qualified for the World Cup twice, in 1982 and in 2010, while Peru have made four World Cup Finals, most recently in 1982. In event of a draw on aggregate, away goals apply.