Jess Ilse from Halifax, received one of the cards, which features a portrait of the princess, and posted a photo of it on Twitter.
The photo was taken by the Duchess of Cambridge and released as part of her birthday celebrations on 2 May.
"The lovely thank you card I received today for Princess Charlotte's birthday," Ilse wrote on Twitter.
"I was excited more than anything when I received the card," Ilse told The Huffington Post UK.
"When you see an envelope in your mailbox with 'Royal Air Mail' stamped on it, you do a little happy dance."