The pair met for the first time at the annual royal garden party in Edinburgh today.
Around 8,000 people attended the event held in the grounds of the Palace of Holyroodhouse.
The Queen, wearing a floral dress and a pink hat, was introduced to a number of guests, including Mr Weir and his wife Kathy.
Alongside MND, they also discussed rugby, while he joked the party had been thrown in celebration of his 48th birthday.
“I mentioned that to her and she had a little giggle,” he said.
“What a fantastic day it is and it’s lovely to be here, and lovely for her to throw a party for my birthday too – very special of her.”
He added: “To meet Her Majesty is pretty special, the knees are still knocking a bit to be fair.”
Mr Weir set up the My Name’5 Doddie Foundation to raise money for research into the causes of MND and investigate potential cures after announcing he was suffering from the disease last year.
The organisation also provides grants to help improve the quality of life for fellow sufferers.
“We know Princess Anne, she’s been a very good support to Scottish rugby and also lately with the MND issue as well,” Mr Weir said.
“Her Majesty knew a bit of the background with the rugby and knew a bit about MND as well.”
He added: “The support and generosity are continuing since the day we announced the MND, the awareness certainly shot up.
“The fight really is on, because at the moment there is no cure. Not yet, as Her Majesty said.”
Mr Weir, who played international rugby for Scotland throughout the 1990s, also chatted with the Queen about changes in the sport.
“She gave a bit of a giggle when I said I didn’t have success over England,” he added.
The garden party was also attended by Prince Andrew and Prince Edward, who joined the Queen in meeting guests on the lawn, under the watchful eye of the Royal Company of Archers and the High Constables of the Palace.
Scotland’s First Minister Nicola Sturgeon also accompanied the royal party.
She attended the event with her husband Peter Murrell and her mentee Charlotte Liddell.