The 63-year-old actor, wearing a fedora hat after revealing a small head wound at the Monuments Men premiere earlier this week, arrived at the screening with co-star Lea Seydoux.
Swinton graced the red carpet in a chic black tuxedo jacket teamed with unusual black tasselled sandals, while Blue Is the Warmest Colour actress Seydoux stunned in a hot pink gown with black embellishment.
Director Wes Anderson and co-stars Tony Revolori, Saoirse Ronan - in an emerald green gown - and Edward Norton - accompanied by wife Shauna Robertson - were also in attendance.
Other guests included Christoph Waltz and Greta Gerwig, both members of the International Jury, and John Hurt with The Host actress Ah-Sung Ko.
The Grand Budapest Hotel is set in the 1920s and revolves around the theft of a priceless Renaissance painting and the struggle over the inheritance of a family fortune.
It follows legendary concierge Gustave H (played by Ralph Fiennes) and his young protégé Zero Moustafa (Revolori).
Jeff Goldblum, Jason Schwartzman, Jude Law, Harvey Keitel, Tom Wilkinson and Willem Defoe also feature in the cast.
Watch the trailer for The Grand Budapest Hotel below: