The rapper shared photos of himself with Sofia Sanchez, who has heart failure, onto Instagram.
He met the youngster at the Lurie Children’s Hospital in Chicago, where she has had open heart surgery.
Along with the photo, he posted the caption: “Me and my love Sofia talking about Bieber and owls and basketball.”
In a blog post on the hospital’s website, it said that Sofia – who turned 11 on Saturday – wanted a new heart and to meet her idol Drake as a birthday wish.
“I’ve been here for seven weeks and I just had open heart surgery because I have heart failure,” said Sofia.
She even did the Kiki challenge – which is performed to Drake’s In My Feelings – in the hope he would see it and meet her.
Drake was in Chicago over the weekend performing two concerts.
In a message to the rapper just before her birthday, Sofia said: “This week’s my birthday and this week’s your concert and I was hoping you could come cheer me up. I did the Kiki challenge.
“When you come here, I can show you. I hope you can come and cheer me up.”
It appeared Drake did just that.
He uploaded another photo showing Sofia smiling wearing a cap with the word “Scorpion” – the name of his latest album – onto Instagram.
Drake is known for acts of kindness.
In February, he gave a young student a $50,000 (£36,000) scholarship after reading one of her essays.
His video for God’s Plan also showed the rapper surprising people in Miami with money – after he decided to give away the entire $1m (£780,000) budget for the video.