You need place a copy of the original header.php file in your child theme, then edit the child’s copy and remove:
<div id="access" role="navigation">
<?php /* Allow screen readers / text browsers to skip the navigation menu and get right to the good stuff */ ?>
<div class="skip-link screen-reader-text"><a href="#content" title="<?php esc_attr_e( 'Skip to content', 'twentyten' ); ?>"><?php _e( 'Skip to content', 'twentyten' ); ?></a></div>
<?php /* Our navigation menu. If one isn't filled out, wp_nav_menu falls back to wp_page_menu. The menu assiged to the primary position is the one used. If none is assigned, the menu with the lowest ID is used. */ ?>
<?php wp_nav_menu( array( 'container_class' => 'menu-header', 'theme_location' => 'primary' ) ); ?>
</div><!-- #access -->