upstream apache {
   server 127.0.0.1:8080;
}
server{
   location ~* ^/service/(.*)$ {
      proxy_pass http://apache/$1;
      proxy_redirect off;
   }
 }

The above snippet will redirect requests where the url includes the string "service" to another server, but it does not include query parameters.

From the proxy_pass documentation:

A special case is using variables in the proxy_pass statement: The requested URL is not used and you are fully responsible to construct the target URL yourself.

Since you're using $1 in the target, nginx relies on you to tell it exactly what to pass. You can fix this in two ways. First, stripping the beginning of the uri with a proxy_pass is trivial:

location /service/ {
  # Note the trailing slash on the proxy_pass.
  # It tells nginx to replace /service/ with / when passing the request.
  proxy_pass http://apache/;
}

Or if you want to use the regex location, just include the args:

location ~* ^/service/(.*) {
  proxy_pass http://apache/$1$is_args$args;
}