The Falcons fly-half faces between four and eight weeks sidelined, having suffered three knee injuries, neck, bicep, groin and appendix problems since his drop-goal saw England crowned 2003 world champions in Sydney.
Newcastle head to Watford on Sunday for a Premiership clash against Saracens, with Shaw lining up in midfield alongside Jamie Noon after England Under-21 international Toby Flood was handed Wilkinson's number 10 shirt.
"We all know Jonny is up there with the best players in the world when he is fit, and all the boys really feel for him. He had such a good pre-season," said Shaw.
"Things happen on the field when he is around, but you could also say the same for Toby Flood, who is a very creative player.
"We've played without Jonny several times before - we have shown we can win without him in the side - and we still have the talent in the team to come away with something on Sunday.
"The good news is that the injury isn't as serious as it could have been, and knowing Jonny, he will just get over whatever obstacles are put in front of him and come back fighting."
Newcastle are without a league away win since February, when they won 9-6 at London Irish, but Saracens have not exactly blasted out of the blocks this season, losing to Wasps then drawing against Bristol.
Former Great Britain and Wigan rugby league captain Andy Farrell features on the Saracens bench, ready for his first taste of Premiership action, while rugby director Alan Gaffney has made several changes following the Bristol result, calling up Rodd Penney, Kameli Ratuvou, Matt Cairns, Kris Chesney and Ben Russell.
"At this point in the season, we've got the situation where a number of guys have yet to play first-team rugby, and they need to be given an opportunity," said Gaffney.
"It is not a rotation policy as such, it is more about giving the players the chance to show what they can do and trying different combinations."
Wasps, buoyant after recording their best start to a league campaign since 1997, should record a third successive victory by toppling Adams Park visitors Harlequins on Sunday.
Quins are without former Wasps centre Stuart Abbott, who is serving a three-week ban, but the home side welcome back England lock Simon Shaw from injury and summer signing Dave Walder has been handed fly-half duties.
Quins' Premiership return has so far not gone according to plan, with defeats against London Irish and Gloucester leaving them among the early strugglers ahead of a tough fortnight that features appointments with Wasps and Leicester.
Sale Sharks boss Philippe Saint-Andre admitted a degree of disappointment following his team's hard-fought 25-13 win at Worcester which took them to the Premiership summit last night.
Sharks edged above Gloucester and Wasps on try-count after subduing the Warriors through touchdowns from centre Chris Bell, flanker Jason White and wing Mark Cueto.
It was a workmanlike effort, especially after Worcester fought back to 15-13 adrift - although there was a sense of frustration after a try bonus point eluded them.
"I am disappointed that we did not get the bonus point," said rugby director Saint-Andre.
"But Worcester away on a Friday night is not an easy game, and I thought we showed a lot of control and courage.
"It was difficult to play rugby when we conceded six successive penalties in the second half - while I don't think Chris Jones deserved his yellow card - but I am pleased with the win."