Practically? Yes. You can create an array of arrays which functions as an 2D array as every item is an array itself:

let items = [
  [1, 2],
  [3, 4],
  [5, 6]
];
console.log(items[0][0]); // 1
console.log(items[0][1]); // 2
console.log(items[1][0]); // 3
console.log(items[1][1]); // 4
console.log(items);

But technically this is just an array of arrays and not a “true” 2D array, as I. J. Kennedy pointed out.

It should be noted that you could keep nesting arrays into one another and so create “multidimensional” arrays.

Something like this?

function listToMatrix(list, elementsPerSubArray) {
    var matrix = [], i, k;

    for (i = 0, k = -1; i < list.length; i++) {
        if (i % elementsPerSubArray === 0) {
            k++;
            matrix[k] = [];
        }

        matrix[k].push(list[i]);
    }

    return matrix;
}

Usage:

var matrix = listToMatrix([1, 2, 3, 4, 4, 5, 6, 7, 8, 9], 3);
// result: [[1, 2, 3], [4, 5, 6], [7, 8, 9]]

Array.fill

Consider using fill:

Array(9).fill().map(()=>Array(9).fill())

The idea here is that fill() will fill out the items with undefined, which is enough to get map to work on them.

You could also fill directly:

Array(9).fill(Array(9))

(important note: Array(9).fill(Array(9)) will fill each row of the array with the same array, so changing one row will change the other rows).

Alternatives to Array(9).fill() include

Array(...Array(9))
[].push(...Array(9))
[].concat(Array(9))
Array.from(Array(9))

We can rewrite the solution a bit more semantically as:

function array9() { return Array(9).fill(); }
array9().map(array9)

or

function array(n) { return Array(n).fill(); }
array(9).map(() => array(9))

Array.from provides us with an optional second mapping argument, so we have the alternative of writing

Array.from(Array(9), () => Array.from(Array(9));

or, if you prefer

function array9(map) { return Array.from(Array(9), map); }
array9(array9);

For verbose description and examples, see Mozilla's Docs on Array.prototype.fill() here.
and for Array.from(), here.

Note that neither Array.prototype.fill() nor Array.from() has support in Internet Explorer. A polyfill for IE is available at the above MDN links.

Partitioning

partition(Array(81), 9)

if you have a partition utility handy. Here's a quick recursive one:

function partition(a, n) {
  return a.length ? [a.splice(0, n)].concat(partition(a, n)) : [];
}  

Looping

We can loop a bit more efficiently with

var a = [], b;
while (a.push(b = []) < 9) while (b.push(null) < 9);

Taking advantage of the fact that push returns the new array length.