The 25-year-old, who made his England debut in March, had been training with the Three Lions ahead of the tournament in Russia, having been named on boss Gareth Southgate's five-man standby list.
However, Tarkowski made the decision to withdraw from the England camp to undergo a hernia operation, from which he is now recovering.
"It wasn't something that had come out of nowhere," Tarkowski told the official Burnley website. "I had been struggling for a while with it and I knew at some point I had to get it done.
"It was just finding the right chance and in a World Cup year and after being called up in the March group, it was a difficult decision to make. But I feel it was the right one to make going into next season.
"It was tough with the England one because I was quite new to it and it never looks well when someone just pulls out of the squad, especially before they even turn up. I felt it was the right thing to do for me to turn up and try my best to get through it.
"But I just didn't feel right and it's not fair on myself or the players there if I'm not 100% and I'm called upon and I want to do myself justice when I'm around that group. This season is more important."
Tarkowski made 33 appearances for Sean Dyche's side last season.