He was criticised on social media for the clip, which was apparently filmed on Christmas Day.
The 32-year-old tweeted his "deepest apologies", saying he loved that his nephew "feels free to express himself".
The video, posted on his Instagram story, shows Hamilton speaking to the camera before turning it on his young relative.
"I'm so sad right now. Look at my nephew," he says.
The camera then shows the boy wearing a pink and purple dress, while holding a toy magic wand.
'Really not acceptable'
Hamilton asks him: "Why are you wearing a princess dress? Is this what you got for Christmas?"
The young boy starts laughing as the British racing driver continues: "Why did you ask for a princess dress for Christmas? Boys don't wear princess dresses."
In response to the video, founder of anti-bullying charity Ditch the Label Liam Hackett tweeted: "Disappointing to see somebody with such a huge platform use it to publicly shame and attempt to undermine a small child."
Meanwhile, Imraan Sathar of discrimination support charity Stay Brave UK, called for the driver to be stripped of his MBE.
Hamilton later apologised for his behaviour and said it was "really not acceptable" to marginalise or stereotype anyone.
The video, which had been uploaded to Snapchat, showed Hamilton's nephew happily dressed up in a princess dress.
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