You have to set the Authorization field in the header.

It contains the authentication type Basic in this case and the username:password combination which gets encoded in Base64:

var username = 'Test';
var password = '123';
var auth = 'Basic ' + Buffer.from(username + ':' + password).toString('base64');
// new Buffer() is deprecated from v6

// auth is: 'Basic VGVzdDoxMjM='

var header = {'Host': ' 'Authorization': auth};
var request = client.request('GET', '/', header);

From Node.js http.request API Docs you could use something similar to

var http = require('http');

var request = http.request({'hostname': '
                            'auth': 'user:password'
                           }, 
                           function (response) {
                             console.log('STATUS: ' + response.statusCode);
                             console.log('HEADERS: ' + JSON.stringify(response.headers));
                             response.setEncoding('utf8');
                             response.on('data', function (chunk) {
                               console.log('BODY: ' + chunk);
                             });
                           });
request.end();

var username = "Ali";
var password = "123";
var auth = "Basic " + new Buffer(username + ":" + password).toString("base64");
var request = require('request');
var url = "";

request.get( {
    url : url,
    headers : {
        "Authorization" : auth
    }
  }, function(error, response, body) {
      console.log('body : ', body);
  } );

An easier solution is to use the user:pass@host format directly in the URL.

Using the request library:

var request = require('request'),
    username = "john",
    password = "1234",
    url = "http://" + username + ":" + password + "@";

request(
    {
        url : url
    },
    function (error, response, body) {
        // Do more stuff with 'body' here
    }
);

I've written a little blogpost about this as well.

for what it's worth I'm using node.js 0.6.7 on OSX and I couldn't get 'Authorization':auth to work with our proxy, it needed to be set to 'Proxy-Authorization':auth my test code is:

var http = require("http");
var auth = 'Basic ' + new Buffer("username:password").toString('base64');
var options = {
    host: 'proxyserver',
    port: 80,
    method:"GET",
    path: '
    headers:{
        "Proxy-Authorization": auth,
        Host: ""
    } 
};
http.get(options, function(res) {
    console.log(res);
    res.pipe(process.stdout);
});

var http = require("http");
var url = "";

var options = {
    host: "",
    port: 80,
    method: "GET",
    path: url,//I don't know for some reason i have to use full url as a path
    auth: username + ':' + password
};

http.get(options, function(rs) {
    var result = "";
    rs.on('data', function(data) {
        result += data;
    });
    rs.on('end', function() {
        console.log(result);
    });
});

I came across this recently. Which among Proxy-Authorization and Authorization headers to set depends on the server the client is talking to. If it is a Webserver, you need to set Authorization and if it a proxy, you have to set the Proxy-Authorization header

This code works in my case, after a lot of research. You will require to install the request npm package.

var url = "";
var auth = "Basic " + new Buffer(username + ":" + password).toString("base64");
exports.checkApi = function (req, res) {
    // do the GET request
    request.get({
        url: url,
        headers: {
            "Authorization": auth
        }
    }, function (error, response, body) {
        if(error)
       { console.error("Error while communication with api and ERROR is :  " + error);
       res.send(error);
    }
        console.log('body : ', body);
        res.send(body);      

    });    
}

For those not using DNS and needs more depth (you can also use request instead of get by simply replacing get with request like so: http.request({ ... })):

http.get({ 
    host: '127.0.0.1',
    port: 443,
    path: '/books?author=spongebob',
    auth: 'user:p@ssword#'
 }, resp => {
    let data;

    resp.on('data', chunk => {
        data += chunk;
    });

    resp.on('end', () => console.log(data));
}).on('error', err => console.log(err));