functions.php

<?php
/*  
 * Shows the event for the first day and remove it from the rest in a multi-day event.
 * Limited to month view only
 *
 * Author: Barry Hughes
 */
function reduce_month_view_single_events( $events ) {
    static $rendered_ids = array();

    foreach ( $events['events']->posts as $index => $post ) {
        if ( in_array( $post->ID, $rendered_ids ) ) {
            unset( $events['events']->posts[ $index ] );

        }
        else {
            $rendered_ids[] = $post->ID;
        }
    }

    remove_filter( 'tribe_events_get_current_month_day', 'reduce_month_view_single_events' );
    return $events;
}

function setup_month_view_single_event_filter( $slug, $name ) {
    if ( $name === 'day' ) {
        add_filter( 'tribe_events_get_current_month_day', 'reduce_month_view_single_events' );
    }
}

add_action( 'tribe_pre_get_template_part_month/single', 'setup_month_view_single_event_filter', 10, 2 );

Just for cross-reference, here are the new solution for Redesigned Views of The Events Calendar

Function - https://gist.github.com/lelandf/3d5e1453de9221c8e4e4293c7787ecbd
Template Override - https://gist.github.com/lelandf/549ec99ea456179dd2256c7613116c41