How to connect Google Cloud SQL from Cloud Functions?

Find your database region and instance name on GCP > SQL > Instances page:

Save your database password into Firebase environment by running:

$ firebase functions:config:set \
    db.user="<username>" \
    db.password="<password>" \
    db.database="<database>"

Then...

db.js

const { Pool } = require('pg');
const { config } = require('firebase-functions');

const project = process.env.GCP_PROJECT;
const region = 'europe-west1';
const instance = 'db';

module.exports = new Pool({
  max: 1,
  host: `/cloudsql/${project}:${region}:${instance}`,
  ...config().db
});

someFunction.js

const { https } = require('firebase-functions');
const db = require('./db');

module.exports = https.onRequest((req, res) =>
  db
    .query('SELECT version()')
    .then(({ rows: [{ version }]) => {
      res.send(version);
    }));

See also https://stackoverflow.com/a/48825037/82686 (using modern JavaScript syntax via Babel)

I found answer in further discussion of #36388165.

disclaimer: this does not seem to be announced officially, so may change afterward. also I only test in mysql. but nature of this solution, I think same way should work as in pg module (it seems to accept domain socket path as host parameter)

EDIT(2017/12/7): google seems to provide official early access, and same method still works.
EDIT(2018/07/04): it seems that there is someone just copy-and-paste my example code and get into trouble. as google says, you should use connection pool to avoid sql connection leak. (it causes ECONNREFUSE) so I change example code a bit. EDIT(2019/04/04): in below example, using $DBNAME as spanner instance name is confusing, I modify example.

in https://issuetracker.google.com/issues/36388165#comment44 google guy says cloud function instance can talk with cloud sql through domain socket in special path '/cloudsql/$PROJECT_ID:$REGION:$DBNAME'.

I actually can connect and operate cloud SQL from below cloud function code.

const mysql = require('mysql');
const pool = mysql.createPool({
    connectionLimit : 1,
    socketPath: '/cloudsql/' + '$PROJECT_ID:$REGION:$SPANNER_INSTANCE_NAME',
    user: '$USER',
    password: '$PASS',
    database: '$DATABASE'
});
exports.handler = function handler(req, res) {
    //using pool instead of creating connection with function call
    pool.query(`SELECT * FROM table where id = ?`, 
                                req.body.id, function (e, results) {
        //made reply here
    });
};

I hope this would be help for those cannot wait for official announce from google.

New Answer:

See other answers, it's now officially supported. https://cloud.google.com/functions/docs/sql

Old Answer:

It's not currently possible. It is however a feature request on the issue tracker #36388165:

Connecting to Cloud SQL from Cloud Functions is currently not supported, as the UNIX socket does not exist (causing ENOENT) and there is no defined IP range to whitelist (causing ETIMEDOUT). One possibility is to whitelist 0.0.0.0/0 from the Cloud SQL instance but this is not recommended for security reasons.

If this is an important feature for you I would suggest you visit the issuetracker and star the feature request to help it gain popularity.