The event, marking Mother's Day in the US, involved around 50 children making gift bags for their mothers.
The prince's appearance was a surprise for the children and their parents.
He also visited an exhibition highlighting the work of a landmine charity supported by his mother, Princess Diana.
Mrs Obama, along with Vice-President Joe Biden's wife Dr Jill Biden, hosted the event in the White House's state dining room to honour military mothers.
It was part of their Joining Forces project, an initiative to encourage Americans to support the military and their families.
Mrs Obama said: "It is an honour to welcome Prince Harry to the White House today.
"As you all may know, Prince Harry is a captain in the Army Air Corps in the British armed forces."
The reference to the prince's military role received a loud cheer from the guests.
The first lady added: "We are absolutely thrilled he could be with us today. He just arrived in DC. He only has a limited time here. But when he heard about this tea and all of you, he wanted to be here to personally thank you for all your service."
By Peter HuntRoyal correspondent
Take one British prince. Place him on American soil. Add some female admirers. And the seeds of "Harry mania" are planted.
It is not Beatlemania. Nothing like it. But it is an indication of the interest there is here in the unmarried son of Diana.
For an ancient institution that needs to be noticed, the cheering of wannabe princesses does not harm.
But from a palace perspective, this trip will have failed if the talk is only about an eligible bachelor and the suitors who want to settle down with him.
The prince - a more complex character than the caricature of a playboy prince conveys - is in the US to focus attention on landmines, on the work being done with injured service personnel, and on some other charities he supports.
That will be his focus in the coming days.  Others, in a land where fairytales are regularly committed to film, may have a different focus.
The White House was a memorable place for his mother, she famously danced with John Travolta at a dinner hosted there by Ronald Reagan in 1985 on her first official visit to the US.
Prince Harry helped the children to construct goody bags including bouquets of roses, edible salted dough jewellery and baked crisps.
Harry also attended an exhibition by the Halo Trust, an anti-landmine charity his mother supported when she visited a minefield being cleared by them in Angola in 1997.
The prince became patron of the Trust's 25th anniversary appeal this year.
The exhibition featured photographs detailing the story of landmines, including an amputee landmine victim, Halo staff clearing ordnance and land cleared from mines being used.
The images came from a range of countries including Sri Lanka, Angola and Afghanistan.
Fiona Willoughby, the Halo Trust's marketing manager, welcomed the prince's presence: "People have forgotten about it and we think Prince Harry following in his mother's footsteps is a worthy cause and will raise the profile of what we are doing.
"He's a soldier he's been to Afghanistan so he understands landmines, he understands conflict and the landmine clearance that's needed."
Prince Harry had previously promoted the charity's work in 2010 in Mozambique, where he detonated mines under supervision and visited victims.
Mrs Willoughby is hopeful that the problem of landmines can be resolved if governments pledge support: "We don't want to be here in another 25 years, we are looking for government support, if it comes and the funds come in the job can be done and we can get it finished."
Prince Harry is in the US on a week-long tour and will also be promoting his own charities and attend the Warrior Games, a sporting championship for injured servicemen and women.
Prince Harry has begun his US tour by meeting Michelle Obama and joining her in honouring America's military mothers at a White House reception.