The 31-year-old was forced off in the seventh minute against Birmingham City on Saturday and will now wear a protective cast for six weeks.
"The news is disappointing for Peter Clarke and the club because he has been a virtual ever-present and a very strong influence on the team since I took charge. It is a big blow for everyone concerned," Terriers manager Mark Robins told the club website.
"Peter has the character to come back quicker than expected and it wouldn't surprise me if he did. Although we can't put an exact timescale on his return, it will be somewhere in the region of 10-12 weeks."