Yousafzai, 27, said the London gig brought back memories of her time with middle school friends and teachers in her Swat Valley homeland, where she said they climbed to the top of a rock and sang Swift's hit song Love Story.
The Pakistani education activist first attracted world attention at the age of 15 in 2012 when she survived a Taliban assassination attempt.
She was shot in her left eye by a gunman after the militant group's leaders agreed to kill her.
She has since spoken around the world to call for access to education for women and girls in countries where it is restricted.
Yousafzai is the youngest person to receive the Nobel Peace Prize, winning it at the age of 17 in 2014 for her work against the suppression of children and young people.
View this post on Instagram A post shared by Malala Yousafzai (@malala)
In her post about attending one of the two Swift concerts this week, Yousafzai said music had been "a gift" after living through a time when it had been banned.
"One of my favourite memories from Swat Valley is a field trip I took in middle school with my best friend, Moniba," she said.
"Moniba and I found the highest rock we could, climbed on top of it and announced to all of our classmates and teachers we were going to perform our new favourite song called Love Story.
"We sang with all of our heart, taking in the joy we felt every second. That's where my Swiftie journey began."
She said it felt magical that her first-ever proper concert would be to see Taylor Swift.
"Three years ago, the Taliban regained power in Afghanistan. Once again, music no longer plays on the streets, and girls and women are barred from school, work and public life," she said.
"In Swat, music made my friends and me feel confident and free. And one day I hope we will live in a world where every girl will be able to enjoy music and live out her wildest dreams."
Swift, 34, is to play three more Eras Tour nights at the national stadium starting on Saturday night, with two more concerts on August 19 and 20.
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