It is Wilkinson's 10th injury since landing the drop-goal to win the World Cup nearly three years ago - since when he has not played international rugby.
"I can't really pinpoint the hit which did the damage," he said.
"I felt it but was able to carry on. I don't think it really hindered the way I was playing.
"The annoying fact is that it seems that playing on may have made it a lot worse.
"What clearly has happened is I must have taken a hit through the front of my stomach which smashed my kidney into a rib, which then lacerated the kidney.
"I was in discomfort throughout the weekend. It was after that I had the scan, which showed quite a bad laceration.
"It's so uncomfortable, training would have been out of the question. I still can't walk without feeling it.
"Kidneys do heal quite quickly, but the specialist has seen the scans and says that I cannot do anything at all for at least a month. I'm so disappointed."