A shofar must be at least a tefach long. The Rishonim disagree about whether this prerequisite is min HaTorah or mid’rabonon. The reason behind this measurement is based on the following: The average width of four fingers pressed together is slightly less than a tefach. When a person blows, part of the shofar must be visible so that people do not think that he is creating the sound from his mouth. A tefach-long shofar is just large enough to slightly protrude from the blower’s fingers.
[שו"ע תקפו, ט, משנ"ב נד, וביה"ל ד"ה ארבעה; ביאורים ומוספים דרשו, 59]