In case you want to dump the hash to a file and load it in your server's code, you can define the following plugin in your webpack.config.js:
const fs = require('fs');
class MetaInfoPlugin {
  constructor(options) {
    this.options = { filename: 'meta.json', ...options };
  }
  apply(compiler) {
    compiler.hooks.done.tap(this.constructor.name, stats => {
      const metaInfo = {
        // add any other information if necessary
        hash: stats.hash
      };
      const json = JSON.stringify(metaInfo);
      return new Promise((resolve, reject) => {
        fs.writeFile(this.options.filename, json, 'utf8', error => {
          if (error) {
            reject(error);
            return;
          }
          resolve();
        });
      });
    });
  }
}
module.exports = {
  // ... your webpack config ...
  plugins: [
    // ... other plugins ...
    new MetaInfoPlugin({ filename: 'dist/meta.json' }),
  ]
};
Example content of the output meta.json file:
{"hash":"64347f3b32969e10d80c"}
I've just created a dumpmeta-webpack-plugin package for this plugin. So you might use it instead:
const { DumpMetaPlugin } = require('dumpmeta-webpack-plugin');
module.exports = {
  ...
  plugins: [
    ...
    new DumpMetaPlugin({
      filename: 'dist/meta.json',
      prepare: stats => ({
        // add any other information you need to dump
        hash: stats.hash,
      })
    }),
  ]
}
Please refer to the Webpack documentation for all available properties of the Stats object.