"Kia ora @jacindaardern!," she wrote.
"It's been a big year for you & [New Zealand] - congrats!"
The 'Diamonds' singer told Ardern her year could "get even better" if she pledged funds to the Global Partnership for Education.
"I hope you & @MFATgovtNZ agree that educating every child can change the world!" she added.
The organisation is working alongside Rihanna's own charity, the Clara Lionel foundation, to provide education for children in poor countries around the world.