How to group mysql results by foreign keys into a single array through a single query?

I believe it solves your grouping issue, but the solution is PDO and PDOStatement

<?php
    $dsn = 'mysql:dbname=testdb;host=127.0.0.1';
    $user = 'root';
    $password = 'senha';

    $pdo = new PDO($dsn, $user, $password);

    $sts = $pdo->prepare("SELECT b.setor, a.grupo_id, a.id, a.ramal, b.gestor
                         FROM tb_ramais a inner join tb_grupos b on a.grupo_id = b.id
                  ORDER BY b.setor");

    $sts->execute();

    $resultado = $sts->fetchAll(PDO::FETCH_NAMED | PDO::FETCH_GROUP);
    print_r($resultado['setorA']); 
    echo '<br>';    
    print_r($resultado['setorB']);
    echo '<br>';

//Setor A
Array
(
    [0] => Array
        (
            [grupo_id] => 1
            [id] => 2
            [ramal] => 2345
            [gestor] => Carlos
        )

    [1] => Array
        (
            [grupo_id] => 1
            [id] => 1
            [ramal] => 1234
            [gestor] => Carlos
        )

)

//Setor B
Array
(
    [0] => Array
        (
            [grupo_id] => 2
            [id] => 3
            [ramal] => 3456
            [gestor] => Jose
        )

    [1] => Array
        (
            [grupo_id] => 2
            [id] => 4
            [ramal] => 4567
            [gestor] => Jose
        )

)

Foreach

foreach ($resultado['setorA'] as $setorA) {
    print_r($setorA);
    print('<br>');
}

Array
(
    [grupo_id] => 1
    [id] => 2
    [ramal] => 2345
    [gestor] => Carlos
)
Array
(
    [grupo_id] => 1
    [id] => 1
    [ramal] => 1234
    [gestor] => Carlos
)

In terms of performance, I believe it will depend on factors, but you can use that peacefully in your projects.

You have already tried to JOIN , in both tables, example:

SELECT
g.setor,
r.ramal,
g.gestor
FROM tb_ramais r
INNER JOIN tb_grupos g
ON r.grupo_id = g.id

SQL Fiddle Example

The result of this query returns:

Array
(
    [0] => Array
        (
            [setor] => setorA
            [ramal] => 1234
            [gestor] => Carlos
        )

    [1] => Array
        (
            [setor] => setorA
            [ramal] => 2345
            [gestor] => Carlos
        )
...

So you can do:

$ramais = array();
foreach ($result as $row){
    $ramais[$row['setor']][] = array('ramal'=>$row['ramal'],'gestor'=>$row['gestor']);
}

And you will have the associative array:

Array
(
    [setorA] => Array
        (
            [0] => Array
                (
                    [ramal] => 1234
                    [gestor] => Carlos
                )

            [1] => Array
                (
                    [ramal] => 2345
                    [gestor] => Carlos
                )

        )
        ...

Then you can work the array as:

foreach ($ramais['setorA'] as $setorA){
    echo $setorA['ramal'];
}

As far as feasibility deta solution, each case is a case, whether we are talking about tens, hundreds, thousands or millions of records.

In response to this comment , in off-topic , even though this is not the Stack Overflow template, but valid in my opinion, so that doubts sourced from a comment made more broadly and completely.