Conte has been taken ill this week after experiencing severe abdominal pains.
The former Inter Milan and Chelsea manager took charge of Spurs over the weekend when they defeated Preston North End 3-0 in the fourth round of the FA Cup.
Conte will be missing from the dugouts when Spurs host champions Manchester City in the Premier League this weekend.
Tottenham also have upcoming games against Leicester City and AC Milan in the UEFA Champions League.
“Antonio Conte recently became unwell with severe abdominal pain,” said a Tottenham statement.
“Following a diagnosis of cholecystitis, he will be undergoing surgery to remove his gallbladder today and will return following a period of recuperation.
“Everyone at the club wishes him well.”
Gallbladder removal surgery, also known as a cholecystectomy, is usually carried out after the formation of gallstones in the bile-storing organ.
The procedure is most often performed as a keyhole surgery, which usually allows patients to leave hospital on the same day or morning after undergoing general anaesthetic, according to the NHS.
The health body adds that people are generally “able to return to most normal activities within two weeks”.