The England management hope he will be fit to face South Africa six days later - but Stransky believes there could be a knock-on effect.
"I don't think it's going to matter hugely in the game against America but in the build-up to the following week's game it does make a difference," said Stransky, whose extra-time drop kick enabled the Springboks to beat New Zealand in the 1995 final in Johannesburg.
Victory over South Africa would almost certainly guarantee England top spot in their group, and with it an easier quarter-final.
But Stransky said: "If Wilkinson's carrying an injury and isn't 100% there is a problem.
"The danger is that he isn't 100% and if you go into a big game carrying an injury then you can come unstuck.
"It all depends how long-term it is. Going into a World Cup you want momentum, certainty and a team that is settled.
"But ultimately Jonny is good enough to slot in and continue where he left off in the last game he played, so if he is fit I don't think it will make that big a difference."