The midfielder, a January signing from Colchester, made his full debut in Saturday's 1-0 win over Blackpool but was forced off after just 35 minutes following a clash with Blackpool goalkeeper Matt Gilks.
Wordsworth will not require surgery but will now need to rest for six weeks before starting to regain his match fitness.
Daryl Murphy picked up a late knock in the weekend victory but is expected to be fine for Tuesday's visit of promotion-chasing Watford.
Meanwhile, winger Lee Martin (hamstring) and goalkeeper Scott Loach (sprained thumb) will both return to contention against the Hornets having missed out of late.
Saturday's success over Blackpool moved Town four points clear of the drop zone.