The 28-year-old, who picked up a Premier League winners' medal while on loan at Leicester City last season, requires surgery to remove extra bone growth in his ankle.
"I am bitterly disappointed," Dyer told the club's official website. "I was feeling good after completing pre-season training and being involved in the friendlies and the first three games of the campaign.
"I started to feel some pain in my ankle after returning from the training camp in America. I saw a specialist last week and the MRI scan revealed the extra bone growth at the back of my ankle.
"There is not a lot I can do about it, but I am determined to work even harder after my operation to play my part for the team on my return."
Dyer, who has made more than 270 appearances since his arrival from Southampton in 2009, signed a new four-year contract at the Liberty Stadium in August.