The man is reported to have fired two shots in the air before escaping, but a spokeswoman for the brand said nobody was injured.
The awards program will be broadcast on Facebook Live that evening.
Anya Taylor-Joy and George MacKay will receive the award from Oscar winner Charlize Theron.
The duchess wore a custom made Alexander McQueen ensemble.
She got married in a bespoke classic lace gown with a high neck, cap sleeves and an open back by Giles Deacon.
The designer created the outfit specifically for the occasion.
The longtime Shibuya establishment says it has few similarities with the American president, aside from its name.
“Girl Starter” is aimed at empowering young female entrepreneurs between the ages of 18 and 24.
Guests included Emilia Wickstead, Natasha Zinko, Courtney Love and Alice Temperley.
The model hit the premiere of “Okja” in Cannes alongside Rihanna, both dressed in Dior.
The tea will be served at the Georgian restaurant on the department store’s fourth floor.