The queen was speaking here at the launch of a book titled "India's Indira: A Centennial Tribute" compiled by the Indian National Congress, comprising articles, essays and photographs of the first woman prime minister of India.
The queen recalled Indira Gandhi for being a powerful woman and a towering personality.
"I still remember her photograph with the then American president Richard Nixon. She wasn't a tall woman, but she was a towering figure.
Remembering the time when Gandhi came "sitting on a yak along with her father," she said the Gandhi family had been on close friendly terms with the Royal Family of Bhutan.
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"I used to admire the white streak of hair she had. Although I was very young, I still wanted that streak of white hair," the queen said.
The book, edited by senior Congress leader Anand Sharma, has several photographs of Indira Gandhi and Jawaharlal Nehru contributed by the royal family.
Talking about Gandhi's leadership, Congress leader and politician-writer Shashi Tharoor said when she had become the first female prime minister of India, many had wondered if she was capable of the job.
"But as it turned out, she became a better leader than many who came after her could only hope to be," said Tharoor, who was here to attend the book launch at the ongoing Mountain Echoes Literary Festival.