The 87-year-old royal thanked Millie Garland, 11, for "sharing her concerns" and said that she would pass on her request to Prime Minister David Cameron.
The youngster sent the letter to Buckingham Palace after watching a bulletin on the sentencing of Michael Adebolajo and Michael Adebowale, explaining that she was upset that Fusilier Rigby's son "would not have a dad anymore" and that something needed to "get done".
The Queen replied to 11 year-old Millie's letter
Less than a week later, she received a reply.
Millie's mum Lucy said, "We're just so proud of her, to take something like that to heart and then to take it to the top. I just thought what a good idea.
"She was upset that anything like that could happen in this country.
"We weren't expecting a reply so when it came it was such a surprise, we couldn't believe it.
"It came in a really posh envelope and we had to find a special knife to open it because we didn't want to damage it."
The youngster was so pleased to have received a letter from the Queen that she took it in to show her classmates at Haydon Wick primary school in Swindon.
"My friends didn't think I would get a reply and they didn't believe me when I showed them the letter," Millie said.
"I do hope something will be done and there will be a day (of remembrance), but if there isn't I won't get upset, I will just accept it.
"I was watching the telly and it came up about Lee Rigby and I was quite upset and angry about how long it was taking to get something done.
"I was just upset about the fact that his little boy won't have a dad anymore, and I thought that something should be done so I decided to write to the Queen about it."
Millie's grandmother Barbara Garland, who helped her pen the letter, said, "I really wasn't expecting her to get a reply at all.
"I didn't even read it because I just thought it would be dropped. The next thing I knew it had been folded up and put in an envelope.
"She was so excited when she rang me to tell me she had got a letter back. She is a very caring and compassionate little girl, about a lot of things."