Malala Yousufzai spoke to the Queen about the importance of education when they met at Buckingham Palace.
The teenager, accompanied by her father Ziauddin, gave the Queen a copy of her book, I Am Malala, during their meeting in the palace's White Drawing Room, telling her: "It is a great honour for me to be here, and I wanted to present you with this book."
Accepting the gift, the Queen replied: "That's very kind of you," before chatting with the teenager for a few moments.
She was reduced to laughter by a comment from the Duke, who quipped that in this country, people want children to go to school to get them out of the house. Malala covered her face while in a fit of giggles at his joke.
Malala Yousafzai has spoken of her experience of settling into her new life in Birmingham.
"I was feeling a little bit embarrassed and worried... the school was quite different compared to school in Pakistan," she said.
She said she was particularly surprised at the level of freedom afforded to women.
"It was difficult to adjust to this new culture and society, especially for my mother, because we have never seen that women would be that much free, that they would go to any market, they will be going alone.
"In our country, if you want to go outside, you must go with a man.
"If even your five-year-old brother goes with you it's fine, but you must have someone else, a girl cannot go outside all alone."
A Pakistani schoolgirl shot by the Taliban for campaigning for girls to have access to education has been tipped for the Nobel Peace Prize.
"I have Malala Yousafzai on top," Kristian Berg Harpviken, director of Oslo-based peace research institute PRIO, told reporters ahead of the annual awards that start today.
Speaking to the BBC's Panorama programme, the 16-year-old said of the prospect:
"If I win Nobel Peace Prize, it would be a great opportunity for me, but if I don't get it, it's not important because my goal is not to get Nobel Peace Prize, my goal is to get peace and my goal is to see education of every child."
The news that Malala Yousafzai has been invited to Buckingham Palace to meet the Queen has fuelled speculation she could be named winner of this year's Nobel Peace Prize.
Bookies are now offering odds of two-to-one that the youngster, who was shot in the head by the Taliban for her campaigning on girls' educational rights, will take home the prestigious award when it is announced on Friday.