The Leeds loanee went under the knife on Saturday while his team-mates earned their first points of the season in a 2-2 draw at Sheffield Wednesday.
Physio Bobby Bacic told the club website: "Steve underwent surgery on his sportsman's hernia and walked out of the hospital unaided later in the evening. In fact he was awake during the double procedure as he wanted to know how we were getting on at Sheffield!
"Steve felt the pain on his right side come on sharply during the last 15 minutes of the match against Huddersfield last weekend.
"Our original plan was to manage him to at least the international break, however during Thursday's training session the pain build-up was such that Steve could not sprint fully.
"We therefore decided to go ahead with surgery as soon as possible and are extremely grateful to the German specialist who agreed to operate in London early, rather than us go to Munich later in the month for the procedure.
"During the operation the surgeon detected the beginning of a very small tear on the left side, so this was also addressed.
"It is too early to give an exact return date as Steve will need to allow the operation sites to settle and avoid infection. However if there are no complications then a return to play within four weeks is a possibility. Steve will remain at our club for his rehab."