Woakes bowled only two overs in Thursday's tournament opener against Bangladesh before leaving the ground, dealing a blow to England's bid to win their first global 50-overs title.
The 28-year-old Finn, who has 102 wickets from 69 one-dayers, will be expected to ease England's pace concerns with Woakes unavailable, Jake Ball struggling and Ben Stokes's problematic knee preventing the all-rounder from bowling spells at full throttle.
England next face New Zealand in Cardiff on Tuesday.