The 25-year-old has been training with the national team since Monday, having been named on the five-man standby list for Gareth Southgate's World Cup squad.
However, any hopes he had of joining team-mate Nick Pope in heading to Russia look to have been dashed, although Burnley expect him to be available for the start of pre-season training.
"James Tarkowski has withdrawn from England's World Cup preparation camp at St. George's Park to undergo a hernia operation," a club statement read.
"Tarkowski is expected to be fit for the Clarets' return to pre-season training in early July."
Burnley added that England do not plan to call up another defender for the remainder of the training camp.
Southgate's side begin their warm-up for the World Cup with a friendly match against Nigeria next Saturday.