The girl, identified as Victoria, wanted to be given telekinetic powers so she could become a dragon trainer, the BBC reported.
She included NZ$5 ($3.20) with her letter, apparently as a bribe.
Writing back on official letterhead, Ardern said: "We were very interested to hear your suggestions about psychics and dragons, but unfortunately we are not currently doing any work in either of these areas.
"I am therefore returning your bribe money, and I wish you all the very best in your quest for telekinesis, telepathy and dragons."
In a handwritten note, Ardern added: "P.S. I'll still keep an eye out for those dragons. Do they wear suits?"
Explaining the niche request, the girl's brother said her interest in telepathy comes from the Netflix sci-fi series "Stranger Things", which features telepathy and telekinesis - the power to move things using one's mind.
This is not the first time Ardern, who gave birth to a daughter last year, has replied to a young girl's letter.
In March, one Twitter user posted a letter that was reportedly sent from Ardern in response to an eight-year-old girl who had said it was a "good idea to ban dangerous guns".
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)