I had the exactly same problem and spent a couple of hours…
I guess you are using older version of nginx (lower than 1.7)?
In nginx 1.7 you can use this directive:
proxy_ssl_server_name on;
This will force nginx to use SNI
Also, you should set the SSL protocols:
proxy_ssl_protocols TLSv1 TLSv1.1 TLSv1.2;
For earlier versions you may be able to use this patch (but I can’t verify that that is working):
http://trac.nginx.org/nginx/ticket/229
2019 Update: You should avoid TLSv1 and TLSv1.1 and disable them if possible. I’ll leave them in the answer as they are still valid for SNI.