Shortcode into widget

Simply create a new widget & register it –

/* Create a new Widget */
class WPSE180059_Widget extends WP_Widget 
{
    public function __construct()
    {
        $widget_ops = array(
            'classname' => 'widget_wpse180059', 
            'description' => __( 'A Custom Widget') 
        );
        parent::__construct('wpse180059', __('WPSE180059 Widget'), $widget_ops);
    }

    public function widget( $args, $instance )
    {
        $title = apply_filters( 
            'widget_title', 
             empty($instance['title']) ? '' : $instance['title'], 
             $instance, 
             $this->id_base 
        );

        echo $args['before_widget'];

        if ( $title )
        { echo $args['before_title'] . $title . $args['after_title']; }

        /* here goes your Shortcode */
        echo do_shortcode('[example]');

        echo $args['after_widget'];
    }

    public function update( $new_instance, $old_instance )
    {
        $instance['title'] = strip_tags($new_instance['title']);
        return $instance;
    }

    public function form( $instance )
    {
        //Defaults
        $title = esc_attr( $instance['title'] ); ?>
        <p><label for="<?php echo $this->get_field_id('title'); ?>"><?php _e('Title:'); ?></label> <input class="widefat" id="<?php echo $this->get_field_id('title'); ?>" name="<?php echo $this->get_field_name('title'); ?>" type="text" value="<?php echo $title; ?>" /></p>
<?php
    }
}

/* Register your Widget */
function WPSE180059_init() {
    register_widget('WPSE180059_Widget');
}
add_action('widgets_init', 'WPSE180059_init');