But much to the surprise of onlookers the Queen returned the gesture by putting her arm round first lady's waist.
The extraordinary scene took place on Wednesday as President Barack Obama made his first visit to Britain as US President. It is forbidden under royal protocol to touch the Queen, reported Daily Mail online.
The American first lady, dressed in a black satin suit skirt, towered over the Queen who was dressed in a soft shade of pink.
The two women seemed to have formed a bond as they chatted and laughed together, with shoes reportedly being one of the topics of discussion.
The American president and his wife presented the Queen with an iPod containing photographs and videos of her last State visit to the US.
The Obamas who are in London for the G-20 summit, had earlier met Prime Minister Gordon Brown and his wife Sarah Brown.
Image: A video grab from television footage shows US First Lady Michelle Obama standing with Britain's Queen Elizabeth during a reception for G20 leaders at Buckingham Palace in London.
Photograph: Reuters/Pool