What about something like (untested, assumption that false, and not undef is a flag for end of data, and that the tree is well-formed (no hashref, for example)):

sub genIterator {
    my $tree = shift;
    my @stack = ( [ 0, $tree ], 0 );
    return sub {
        my $work     = shift( @stack );
        while ( ref( $work ) ) {
            my $index    = $work->[0];
            my $worktree = $work->[1];

            if ( $index >= scalar( @{$worktree} ) ) {   # Update 3
                $work = shift( @stack );
                next;
            }
            elsif ( ! ref( $worktree->[$index] ) ) {
                unshift( @stack, [ $index+1, $worktree ] );
                return $worktree->[$index];
            }
            else {
                unshift( @stack, [ $index+1, $worktree ] );
                $work = [ 0, $worktree->[$index] ];
                next;
            }
         }
         return;     # empty stack
    }
}
[download]

Test Code:

my @data = [ [ 0 ], 1, 2, [ 3, 4, 5 ], 6, [ 7, 8, [ 9, 10 ], [ 11, [ 1
+2 ], 13 ], ], 14 ];

my $it = genIterator( \@data );

use DDP;
p @data;

while (defined( my $x = $it->() )) {
    say $x;
}
__END__
[
    [0] [
        [0] [
            [0] 0
        ],
        [1] 1,
        [2] 2,
        [3] [
            [0] 3,
            [1] 4,
            [2] 5
        ],
        [4] 6,
        [5] [
            [0] 7,
            [1] 8,
            [2] [
                [0] 9,
                [1] 10
            ],
            [3] [
                [0] 11,
                [1] [
                    [0] 12
                ],
                [2] 13
            ]
        ],
        [6] 14
    ]
]
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
[download]

Update: No longer need to assume that '0' is an invalid element, but the use of the iterator needs to be adjusted.

Update 2: Compared to Eily's solution, mine is iterative (non recursive), while Eily's is recursive.

UPdate 3: changed '>' to '>=' after testing, added test code.