This is a classic case of where early-return makes sense....

There are some schools of thought that suggest early return is a bad thing, but consider changing all your if (isWon) {break;} statements to be return winner;.

We can get rid of the iswon and the winner variables entirely, as well as the then unnecessary checks to gate each logic loop. Your method looks like:

public Player getWinner() {

    // check columns (same x)
    for (int x = 0; x < fields.length; x++) {
        Player value = fields[x][0];

        if (value == null) {
            continue;
        }
        for (int y = 1; y < fields[x].length; y++) {
            Player current = fields[x][y];
            if (current == null || !current.equals(value)) {
                break;
            }
            if (y == fields[x].length -1) {
                //  Early Return.... We have a WINNER!
                return value;
            }
        }
    }
    // there was no winner in this check
    // no need for isWon check or variable... we can't get here unless there is
    // no winner yet....
    for (int y = 0; y < fields[0].length; y++) {
            Player value = fields[0][y];
            if (value == null) {
                continue;
            }
            for (int x = 1; x < fields.length; x++) {
                Player current = fields[x][y];
                if (current == null || !current.equals(value)) {
                    break;
                }
                if (x == fields.length -1) {
                    // We have a winner!
                    return value;
                }
            }
        }

    }
    // and so on....
    ....

    // there is no winner.
    return null;
}