The art exhibition brought together about 200 works from public collections and spans over 500 years.
The exhibition also marks the 250th anniversary of the Royal Academy which was founded in 1768.
When arriving at the event, Meghan was seen closing her own car door - which has prompted an outpouring on Twitter.
After shaking hands with one of her hosts for the evening, Meghan casually shut the car door and headed inside.
'First time I’ve seen an on-duty princess shut her own car door…' wrote one Twitter user.
The Sun‘s royal correspondent Emily Andrews added, 'A princess who still takes the time to shut her car door. Well done Meghan!'
This marks the first time the 37-year-old former actress has carried out a royal engagement on her own, and comes just days after she launched her charity cookbook, Together: Our Community Cookbook at Kensington Palace alongside her mother Doria Ragland and husband Prince Harry.
Meghan will fly to Australia with Prince Harry on October 16, which will be their first overseas tour as a married couple.