Reid is unlikely to feature in Saturday's Premier League derby against Aston Villa at the Hawthorns after taking a knock in the same area as a late substitute in Tuesday's 1-0 FA Cup third round replay loss at home to Queens Park Rangers.
"Steven went to see the doctor this morning," said Clarke who is hoping the Irishman will be back in training next week.
"He has been out for a number of weeks and we didn't release the full nature of the injury. It was a fractured fibula against Arsenal and he effectively played 45 minutes with a broken leg. That tells you the character of the boy.
"He came back on Tuesday and got another knock in the same area. It's not serious but he'll probably miss the weekend and that will be more our decision than Steven's.
"We're trying to protect Steven from himself a little bit," Clarke added on the club's website.
Clarke will decide on Friday whether Argentina midfielder Claudio Yacob, who has missed eight games with a hamstring problem but has trained this week, is ready to face Villa.
Strikers Shane Long (dead leg) and Marc-Antoine Fortune (hamstring) are rated 50-50 while Youssouf Mulumbu is on African Nations Cup duty with DR Congo although fellow midfielder Chris Brunt has recovered from flu and is available.
"Claudio's been out for six weeks and he's working well, but this game might be too close for him," Clarke said. "I'll look at him again tomorrow and I'll make my decision after training.
But he's in the squad and he's in a good place.
"I gave quite an optimistic report in midweek on the injury front. I've got to be honest, Shane hasn't progressed as we'd hoped and is still 50/50."
West Brom are seventh with 33 points from 22 games and chasing European football for next season while Paul Lambert's Villa have slipped into the relegation zone with 19 points.