I have already found I can display one specific month, using the shortcode:
[events_calendar month="09" year="2013"]
…but stil wondering if there’s a way for the widget to automatically search for the next even and display that. If not, this is a workaround that’s not too difficult, I guess
maybe you can try this plugin http://wordpress.org/extend/plugins/php-code-widget/screenshots/ and then use do_shortcode for events_calendar
e.g.
get the next month using php and then add it to the month attribute