In the template, Modify User Option Templates / modifyprofile find and remove this bit of code.
<fieldset class="blockrow">
<legend>{vb:rawphrase instant_messaging}</legend>
<ul class="group">
<li>
<label for="icq">{vb:rawphrase icq_number}:</label>
<input type="text" class="primary textbox" id="icq" name="icq" value="{vb:raw bbuserinfo.icq}" maxlength="30" dir="ltr" tabindex="1" />
</li>
<li>
<label for="aim">{vb:rawphrase aim_screen_name}:</label>
<input type="text" class="primary textbox" id="aim" name="aim" value="{vb:raw bbuserinfo.aim}" maxlength="30" dir="ltr" tabindex="1" />
</li>
<li>
<label for="msn">{vb:rawphrase msn_messenger_handle}:</label>
<input type="text" class="primary textbox" id="msn" name="msn" value="{vb:raw bbuserinfo.msn}" maxlength="50" dir="ltr" tabindex="1" />
</li>
<li>
<label for="yahoo">{vb:rawphrase yahoo_messenger_handle}:</label>
<input type="text" class="primary textbox" id="yahoo" name="yahoo" value="{vb:raw bbuserinfo.yahoo}" maxlength="30" dir="ltr" tabindex="1" />
</li>
<li>
<label for="skype">{vb:rawphrase skype_name}:</label>
<input type="text" class="primary textbox" id="skype" name="skype" value="{vb:raw bbuserinfo.skype}" maxlength="32" dir="ltr" tabindex="1" />
</li>
</ul>
<p class="description">
{vb:rawphrase may_enter_identity_for_im}
</p>
</fieldset>