Wearing only his pyjamas and a dressing gown, the little prince shook hands with Barack as his proud dad, William watched on.
Former First Lady Michelle was also crouched down next to her husband to greet the mini royal.
While the rules were bent for George, it's unlikely Archie will meet any world leaders until he's a grown up.
Meghan and Harry have kept Archie out of the public eye so far, sharing only a few images to the Instagram of the tiny tot.
The couple are said to be heading on a royal tour later this year, so royal fans should catch a glimpse of Archie during that time.
His christening is also said to be happening in July, which will be another occasion where royal watchers hope to see the littlest royal.