Reid made his comeback as a substitute during Tuesday's FA Cup defeat against QPR at the Hawthorns, with West Brom having kept the extent of the Irish international's injury under wraps until now.
Clarke said: "We didn't release it a the time, but it was a fractured fibula Steven got against Arsenal. He played for 45 minutes with a broken leg, which shows the character of the boy. I've put it out there now because I want people to know that.
"Sometimes people think 'Steven is always injured' but he has been unlucky. He's had a number of serious injuries, but he has an incredibly strong mental strength and he wants to play. He keeps saying 'I'm okay, gaffer'."