Dr David Nott recalled how he was unable to reply when she asked him about his experience in Aleppo at a lunch at Buckingham Palace.
Sensing he was "seriously traumatised", the Queen asked if she could help before calling for her corgis.
He told Desert Island Discs the dogs had a therapeutic effect.
The surgeon, who volunteers with Medecins Sans Frontieres and the International Committee of the Red Cross, said the Queen's humanity was "unbelievable" and described her as "warm and wonderful".
Dr Nott told the BBC Radio 4 programme that he had been operating on "badly damaged" children from a makeshift theatre in the Syrian city and key battleground of Aleppo, and he did not know what to say to the Queen when it was his turn to speak.
For more than two decades, Dr Nott - a consultant surgeon at Royal Marsden, St Mary's and Chelsea and Westminster Hospitals in London - has given up several months every year to volunteer in war zones and amid major humanitarian crises.
He has performed life-saving surgery in Afghanistan, Bosnia, Iraq, Libya, Pakistan and Syria.
During Desert Island Discs he recalled meeting the Queen at a private lunch at Buckingham Palace in October 2014.
Dr Nott - who admitted that he suffered from Post Traumatic Stress Disorder as a result of his work in war zones - said: "I [had been] coping [in Syria] with children that were really badly damaged and she must have detected something significant.
"I didn't know what to say. It wasn't that I didn't want to speak to her - I just couldn't. I just could not say anything.
"She picked all this up and said, 'Well, shall I help you?' I thought, 'How on earth can the Queen help me?'
"All of a sudden the courtiers brought the corgis and the corgis went underneath the table."
Dr Nott said the Queen then opened a tin of biscuits and invited him to feed and stroke the dogs.
He added: "And so for 20 minutes during this lunch the Queen and I fed the dogs. She did it because she knew that I was so seriously traumatised. You know the humanity of what she was doing was unbelievable."
During the programme, Dr Nott also recalled the moment when he was operating on a man and six armed militants from so-called Islamic State (IS) burst into the room.
Dr Nott said he was too scared to speak for fear that the militants would recognise he was British.
"I remember so vividly my legs shaking like jelly, and they stayed in for about 20 minutes with their guns all pointing towards us, then all of a sudden something happened outside... and they left," he said.
Earlier this year, Dr Nott was named winner of the Robert Burns Humanitarian Award 2016.
He also set up the David Nott Foundation which offers other surgeons and medical professionals training and advice on how to help in conflict and natural disaster zones around the world.

He is the highest-ranking US official to publicly implicate Beijing since news of the data breach emerged.
China always dismissed suggestions that it was behind the hacking.
The statement comes after three days of high-level talks in which China and the US agreed to a "code of conduct".
"China remains the leading suspects," said Mr Clapper at a conference in Washington DC, but "the US government continues to investigate" he added, according to his office.
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At the Washington talks where cyber security was a top priority, US Secretary of State John Kerry said there was a need to work with China to develop a "code of conduct" on state behaviour in cyberspace - Chinese representatives had agreed with these conclusions.
"It's something that we agreed needs to be addressed and hopefully it can be addressed soon," State Department spokesman John Kirby said on Thursday.
China has said any suggestion that it was behind the hacking is "irresponsible and unscientific".
A war surgeon has told how the Queen helped him overcome trauma by allowing him to pet her corgis, days after he returned from Syria.
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China is the "leading suspect" in the massive hack of a US government agency holding the personnel records of millions of Americans, US intelligence chief James Clapper has said.