The 2001 and 2005 Test Lion, who had been selected in Martin Johnson's original 44-man squad for the trip to Australasia, limped off injured after just 50 minutes of Toulon's European defeat to Cardiff Blues in Marseilles.
"I'm not sure if it's a cracked rib. It feels like a bit of a back strain and I will find out this week," said Wilkinson, who went down in a heap after kicking an unsuccessful penalty attempt just two minutes after being on the wrong end of a heavy tackle.
"At the moment it does feel a bit uncomfortable but I am not in a position where I am feeling dread in any way.
"From what the physio said, I hope it is run of the mill, that I can have some treatment and be raring to go."
Wilkinson's injury seemed to be the turning point at the Stade Veledrome, with the Blues scoring three tries in his absence to secure a 28-21 win.
The World Cup winning fly-half refused to back up those suggestions, however, and was instead keen to praise the support from close to 50,000 local fans.
"It's an absolute pleasure (to play for Toulon's fans), like I've said before," added Wilkinson.
"There's nothing that you can substitute for the feeling of playing for the love of doing that and wanting to pay back a load of people that will support you until the end of the earth.
"These guys will always be there with us. This club is part of the region, it's part of the life here in Toulon, and long may that continue."
The past two weekends have brought a huge amount of disappointment for Wilkinson and co, with Sunday's defeat coming just days after their Top 14 dream came to an end with an extra-time reverse at the hands of Clermont Auvergne.
But while Wilkinson admits he would rather have finished the season on a high, he insists this star-studded Toulon squad will be stronger for the heart-breaking experience.
"It was disappointing but it's the experience we need.
"Over the season, we've perhaps been a bit inconsistent. We've done some really good things but, at the last minute when the game's been tough, we've maybe fallen foul.
"It's important that we learn those lessons now and make the changes. We know that, with these guys and the spirit we've got, we'll make it happen."