It poses a problem for Taylor, who has no other natural left backs in his squad.
Mark Lynch, usually a right back, came on for Dawson today, while Damien Delaney has also covered the position this season.
Roland Edge would have been the obvious replacement, but he was released by the club yesterday. The Gillingham-born left back has also been struggling with injury, and Taylor says it was "in the best interests of everybody if he went back down south and got himself fit again."
The City boss has yet to decide if he will move into the transfer market to find a new left back, so soon after the news of Dawson's injury.
He does have Marc Joseph, a right-sided defender, back in his squad after his loan spell at Bristol City came to an end. Centre back Danny Coles will also be back in the next few weeks after injury.