Gilkes, who is the co-founder of online art auction house Paddle8 and close friend to the Royal Family, also posted photos from their pair's trip.
It is the first time the couple have shared glimpses into their relationship since being linked in January.
However, Sharapova, who previously dated fellow tennis star Grigor Dimitrov, continues to keep her relationship to the Etonian millionaire relatively low profile.
Sharapova fell from grace in 2016 when testing positive for a banned substance at the Australian Open, which led to her serving a 15- month doping ban.
Last year she admitted to having gone on a dating spree during her drugs ban, but said men typically found her "too intimidating."