He told the club website: "I took a shot at goal and felt my ankle give way. It's very frustrating."
Norris, 29, is less of a concern, and is likely to recover from a back injury before the start of the new campaign.
Boss Roy Keane added: "Chuck [Norris] is a concern for us as well. He has got a stiff back and you have to be careful with that type of problem.
Maybe a blessing in disguise. Yes we will miss a truly vital player but that keeps him injured for the whole of the transfer window.
Wickhamisoursaviour
"He won't play over the next few days and will be touch and go for the West Ham game at the weekend."
Wickham had been seen as an answer to Town's scoring problems after his impressive performances for the England Under-17s at this summer's European Championships.
Keane's men struggled to score goals last season, especially at Portman Road, and have yet to make additions to their forward line.
Source: BBC Sport
Source: BBC Sport