As Marc B stated, wp isn't sending json. You need to set the content type in the headers, and also send it as json:
$body = array('api_key' => 123);
$headers = array (
'Accept' => 'application/json',
'Content-Type' => 'application/json',
'Content-Length' => strlen(json_encode($body)
);
$args = array(
'method' => 'POST',
'headers' => $headers,
'body' => json_encode($body)
);