The Australian-born royal's father, John Donaldson, died in Hobart at the age of 84 on Saturday. His health had declined in recent years.
Queen Mary and her husband, King Frederik, had the chance to spend "precious time" with him last month at the end of a six-day state visit to Australia.
"My heart is heavy, and my thoughts are grey. My beloved father has passed away," Queen Mary said in an Instagram post.
"But I know that when the grief settles, the memories will brighten my day, and what will remain strongest is love and gratitude for everything he gave me and taught me."
Mr Donaldson, a professor of applied mathematics, was born in Scotland in 1941 and later moved to Australia in 1963 with his wife, Henrietta. They became Australian citizens in 1975. He lost his wife in 1997.
In 2001, he remarried, to a British author named Susan Horwood who writes crime novels under the pen name Susan Moody.
The Danish royal house's website has opened a digital condolence book where people can write messages.
Acting Danish prime minister Mette Frederiksen expressed deep condolences to Queen Mary and her family.
"The Danish people came to know John Donaldson when, with pride and warmth, he walked his daughter up the aisle and gave Denmark its Crown Princess," she said in a statement.
"We will never forget that."
Professor Donaldson wore a kilt and beamed as he gave his daughter away during the church wedding ceremony at Copenhagen Cathedral on May 14, 2004.
Queen Mary is the youngest of Professor Donaldson's four children, sister to Jane, John, and Patricia.Â
He is also survived by 12 grandchildren, including Crown Prince Christian, who will one day become the Danish king.
The family will hold a private memorial service.
