The winger had to be substituted after just 26 minutes of the the goalless draw at Spotland and is an early doubt ahead of the trip to Dagenham & Redbridge on Saturday.
City assistant manager Steve Parkin told the club's official website: "Reidy was off balance on one leg and their lad caught him from the other side. I think he over-stretched and felt something go in his groin. He was certainly very sore when he came off.
"It is important that we get him assessed early enough. Matty (Barrass, head physio) will have a look at him and we will have a better idea on the situation towards the back end of this week.
"I would believe that he would certainly be a doubt for the weekend at this stage. It is a shame because he has been fit and on his game recently."