I’ve got the same issue. Deactivating & reactivating Woocommerce plugin didn’t help.
In the console I see a successful AJAX call:
REQUEST HEADERS:
POST /mydomain.fi/wp-admin/admin-ajax.php?action=woocommerce_shipping_zone_add_method HTTP/1.1
Host: localhost
Connection: keep-alive
Content-Length: 64
Accept: application/json, text/javascript, */*; q=0.01
Origin: https://localhost
X-Requested-With: XMLHttpRequest
User-Agent: Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/51.0.2704.103 Safari/537.36
Content-Type: application/x-www-form-urlencoded; charset=UTF-8
Referer: https://localhost/mydomain.fi/wp-admin/admin.php?page=wc-settings&tab=shipping&zone_id=1
Accept-Encoding: gzip, deflate
Accept-Language: fi-FI,fi;q=0.8,en-US;q=0.6,en;q=0.4
Cookie: [cookies removed]
RESPONSE HEADERS:
HTTP/1.1 200 OK
Date: Tue, 21 Jun 2016 07:40:04 GMT
Server: Apache/2.4.7 (Ubuntu)
X-Powered-By: PHP/5.5.9-1ubuntu4.17
Access-Control-Allow-Origin: https://localhost
Access-Control-Allow-Credentials: true
X-Robots-Tag: noindex
X-Content-Type-Options: nosniff
Expires: Wed, 11 Jan 1984 05:00:00 GMT
Cache-Control: no-cache, must-revalidate, max-age=0
Pragma: no-cache
X-Frame-Options: SAMEORIGIN
Content-Length: 66
Keep-Alive: timeout=5, max=100
Connection: Keep-Alive
Content-Type: application/json; charset=UTF-8
RESPONSE BODY
{"success":true,"data":{"instance_id":0,"zone_id":1,"methods":[]}}