"Do you have a date for the party?" the puppet asks the future royal.
With three years to go before she would meet Prince Harry, Meghan joked: "No, you must sit with me!"
The unlikely duo then laughed and excitedly walked off arm-in-arm.
The throwback video comes just months after the Duke and Duchess of Sussex announced their surprise decision to step back as senior members of the royal family.
Since splitting their time between the UK and Canada, Meghan has begun to carve her post-royal career with a series of surprise charity visits.
A mere matter of days after declaring their big news, the new mother visited two local women's charities in Vancouver: Downton Eastside Women's Centre and Justice for Girls.
With a rumoured Disney voiceover deal also in the works, the future looks bright for the former Suits star.