Edit in JSFiddle

HTML
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en">
<head>
    <script src="http://ajax.googleapis.com/ajax/libs/jquery/1.4.1/jquery.js"></script>
    <script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jqueryui/1.8.14/jquery-ui.min.js"></script>
    <link rel="stylesheet" type="text/css" media="screen" href="http://ajax.googleapis.com/ajax/libs/jqueryui/1.8.14/themes/base/jquery-ui.css">
<script type="text/javascript">
$(function() {
    var startDate;
    var endDate;
    
    var selectCurrentWeek = function() {
        window.setTimeout(function () {
            $('.week-picker').find('.ui-datepicker-current-day a').addClass('ui-state-active')
        }, 1);
    }
    
    $('.week-picker').datepicker( {
        showOtherMonths: true,
        selectOtherMonths: true,
        onSelect: function(dateText, inst) { 
            var date = $(this).datepicker('getDate');
            startDate = new Date(date.getFullYear(), date.getMonth(), date.getDate() - date.getDay());
            endDate = new Date(date.getFullYear(), date.getMonth(), date.getDate() - date.getDay() + 6);
            var dateFormat = inst.settings.dateFormat || $.datepicker._defaults.dateFormat;
            $('#startDate').text($.datepicker.formatDate( dateFormat, startDate, inst.settings ));
            $('#endDate').text($.datepicker.formatDate( dateFormat, endDate, inst.settings ));
            
            selectCurrentWeek();
        },
        beforeShowDay: function(date) {
            var cssClass = '';
            if(date >= startDate && date <= endDate)
                cssClass = 'ui-datepicker-current-day';
            return [true, cssClass];
        },
        onChangeMonthYear: function(year, month, inst) {
            selectCurrentWeek();
        }
    });
    
    $('.week-picker .ui-datepicker-calendar tr').live('mousemove', function() { $(this).find('td a').addClass('ui-state-hover'); });
    $('.week-picker .ui-datepicker-calendar tr').live('mouseleave', function() { $(this).find('td a').removeClass('ui-state-hover'); });
});
</script>
</head>
<body>
    <div class="week-picker"></div>
    <br /><br />
    <label>Week :</label> <span id="startDate"></span> - <span id="endDate"></span>
</body>
</html>