"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.
Ms Ardern responded to Rihanna some hours after the initial tweet was sent, highlighting $9 million New Zealand has recently pledged to support access to education in the Pacific.
Kiwi fans of the singer expressed their excitement about the exchange in the comments section.
"Omg, sis knows it's just been Maori language week," one follower wrote.
"Jacinda Ardern be walking into the Beehive like 'yeaahh Me & Riri, we homies!" said another.