The Dutchman, who underwent heart surgery earlier this year, was in seventh place on the overall standings but chose to leave the race in order to be with his wife.
"My pregnant wife has undergone surgery twice this past week," Gesink said in a statement on the team website. "Her situation has not improved and she is still in the hospital. I will immediately leave the Vuelta to be with my family, who needs me right now."
Belkin expressed its support for Gesink's decision to be by his wife's side. The team also added that it "wishes them all the best in this difficult time."