Purse, 33 last week, missed Saturday's 1-0 home defeat by Ipswich, leaving James O'Connor to take over as captain.
"He got injured in the early stages of training on Thursday," said boss Alan Irvine. "It looks like he will be out for two or three weeks.
"With only six defenders to cover four positions, we were always likely to be vulnerable to injury and suspensions."
Purse has played 28 times for Wednesday since signing in May following his release by Cardiff City, taking his career tally past the 500-game mark.
Wednesday won five of their first seven matches following the appointment of new boss Alan Irvine on 8 January.
But they have now lost their last two - both at Hillsborough - to relegation rivals Ipswich Town and Doncaster Rovers, to leave themselves 21st in the Championship table, just a point clear of trouble.
Source: BBC Sport
Source: BBC Sport