The left-back limped off towards the end of City's win at Canvey Island on Friday, and a scan this week will reveal the extent of his knee ligament damage.
Manager Peter Taylor revealed: "Andy's injury is the only negative from the last few days because everything has been going so well.
Dawson Injury Blow
"It is a blow. He's going to get a scan but it's not looking too good and it could be anything from two to six weeks.
"It will definitely put him out of the next three or four friendlies and obviously he's going to miss a lot of work so he's got to be doubtful for the start of the season. We've got to be realistic about the situation.
"He was just settling in. He's done outstandingly well. I knew he was a good player but he's even better than what I thought.
"We'll just keep our fingers crossed and hope it's not too bad. We do have other options for left-back and it could be we'll have to have a look at them."
In fact, City's squad is overflowing with left-back options. Damien Delaney would be the obvious option after being the first-choice left-back for most of last season.
Transfer-listed pair Shaun Smith and Andy Holt could be given a second chance, but neither have played a pre-season game yet.
20-year-old defender Steve Burton could also be given his break after making just a handful of league appearances so far. Burton is currently on the sidelines with a slight groin strain but should be back in action soon. He missed the Canvey game, while Justin Whittle, Alan Fettis and Richie Appleby also sat it out with knocks. All four are hoping to be fit enough to play a part in Neil Mann's testimonial match against Grimsby tomorrow.
In fact, City's squad is overflowing with left-back options. Damien Delaney would be the obvious option after being the first-choice left-back for most of last season.
Transfer-listed pair Shaun Smith and Andy Holt could be given a second chance, but neither have played a pre-season game yet.
20-year-old defender Steve Burton could also be given his break after making just a handful of league appearances so far. Burton is currently on the sidelines with a slight groin strain but should be back in action soon. He missed the Canvey game, while Justin Whittle, Alan Fettis and Richie Appleby also sat it out with knocks. All four are hoping to be fit enough to play a part in Neil Mann's testimonial match against Grimsby tomorrow.