Newcastle United fullback
The 25-year-old defender limped off during the first half of last weekend's 1-1 Premier League draw with Aston Villa unsure whether he had strained or torn his hamstring.
However, the results of a scan have revealed the full extent of the damage and the former Manchester United player is now hoping to limit his absence to as short a spell as possible.
"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."
Simpson's misfortune struck at just the wrong time for both the right-back and manager
The Magpies spent the northern summer attempting to add another defender to their squad, with Lille's Mathieu Debuchy and FC Twente's Douglas firmly in their sights, but were unable to strike a deal for either.
As a result, the injuries which have struck during the last week or so have proved costly and left Pardew having to ask midfielder Vurnon Anita to drop into the back four at the weekend.
The enforced lay-off is particularly frustrating for Simpson, who spent much of the transfer window at the centre of speculation that he could leave the club as he entered the final year of his existing contract with no extension agreed.
However, a man who is not used to missing games is consoling himself with the fact that the break for international matches means the coming weekend would have been blank anyway.
He said: "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."
English Premier League