The 25-year-old defender limped off during the first half of Sunday's 1-1 Premier League draw with Aston Villa unsure whether he had strained or torn his hamstring.
Danny Simpson: "It's a lot better than I first thought.
"I have never had a hamstring problem before. I just felt something bad and I knew straight away I would have to come off.
"But the scan results came back on Wednesday and it is hopefully three weeks, maybe four maximum.
"It depends on each person, their body and how quickly they recover, but it's a lot better than what we first thought.
"Already I'm walking easier than I was on Sunday, so that's a good sign.
"Injuries are part and parcel of being a footballer, but I'm not used to it - I haven't had many injuries.
"For a long time, I haven't really had any issues in that area. It's just one of those things, though.
"With there not being a game for two weeks, if there is a time to have a little niggle then it's probably now.
"I will just have to see how it is at the start of next week and take it from there, but hopefully I won't miss too many games."