The Republic of Ireland international was ruled out of the midweek loss at Tottenham and is also set to be on the sidelines for the FA Cup tie with Cardiff and the Barclays Premier League encounter with Norwich.
Long is the Baggies' joint top scorer with five goals this season after his summer move from Reading.
He told the Wolverhampton Express and Star: "I had an injection yesterday to speed things up but it's very tender at the moment. I'm not training.
"Hopefully it's only going to take a week or two and it's no more serious than that.
"The injection is designed to kill the pain so I can start on my rehab. I'm going to try to aim to be fit for the Norwich game, but that might be a bit too soon."
Long had required a painkilling injection to play against Everton last weekend.