Reid returned to the Baggies side in their 1-0 defeat to Queens Park Rangers on Tuesday night, but the nature of the injury picked up at the Emirates Stadium has only just been made public by Clarke.
Clarke told reporters: "He played for 45 minutes with a broken leg, which shows the character of the boy. We didn't release the injury but it was a fractured fibula he got against Arsenal.
"I've put it out there because I want people to see the character of the boy.
"Sometimes people think 'Steven is always injured' but he has an incredible strong mental strength and he wants to play."
The 31-year-old has made six appearances for West Bromwich Albion this season.