The pair are among nine World Cup squad members currently injured, with the tournament opener against Italy in Rome less than four weeks away.
Wilkinson admits his recovery from shoulder trouble is a patient 'day-to-day' process, while Dawson suffered a jarred left shoulder during a second-team fixture between Northampton and Leicester.
There was further concerning news for England head coach Sir Clive Woodward with Sale Sharks fly-half Charlie Hodgson - Wilkinson's understudy last season - facing at least two weeks out because of a knee injury.
While Hodgson has not suffered a recurrence of the knee ligament damage which destroyed his World Cup dream, specialists want to take another look at him in a fortnight's time.
Hodgson was hurt in European Cup action for his club Sale Sharks and underwent a scan.
"Charlie has not had a recurrence of the ligament injury that required an operation last year, and which kept him out of the game for several months, but he has a recurring problem with the cartilage, " Sharks coach Jim Mallinder confirmed.
"There is no need for surgery at present, but his progress will be reviewed by his specialist in two weeks' time. That means he won't be available for next Sunday's European Cup game against Biarritz."
If Wilkinson and Hodgson are both absent from England's Italian job on February 15 then Woodward faces a probable choice between Paul Grayson, Alex King and Olly Barkley to wear the number 10 jersey.
Northampton, meanwhile, have ruled Dawson out of the European Cup appointment with Agen and say he is likely to miss the crunch European clash against Llanelli on Sunday week.
That would leave him with just one game - an English Premiership fixture against Rotherham on February 7 - to prove his fitness before the Italian encounter.
With Wilkinson's club Newcastle out of the European Challenge Cup competition, Falcons' next scheduled match is also on February 7 - against Gloucester at Kingsholm.
For Dawson, especially, the latest injury setback is deeply frustrating. The run-out was his first appearance since sustaining a calf-muscle injury just before Christmas.
He hurt his shoulder in injury time, after earlier kicking a conversion as Northampton Wanderers beat Leicester Extras 19-18.
Dawson, one of the candidates to succeed Martin Johnson as England captain, had treatment after the game - and it is understood that a two or three-week lay-off now seems likely.
Wilkinson is continuing a slow rehabilitation, having played less than an hour's rugby since he kicked England to World Cup glory two months ago.
"I have not set a date for my return," he said.
"I am going day by day.
"I had the stinger symptoms. But they were slightly more severe, longer lasting, more painful and they spread to more areas.
"It's given me some distress down my right side; it's just weak and it is taking me some time to get the strength back."
Woodward is likely to announce a Six Nations training squad early next week.