It works, but it’s surprising. I had to blink and stare for a moment before I noticed that it actually does do what you intended. All in all, considering the other things I mentioned, I’d write the loop like this:

while ( <INFILE> ) {
    next if not /ver = '(.*?)'/;
    $old_version = $1;
    close INFILE;
    last;
}
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Better yet, if you just opened the file:

{
    open my $fh, '<', $filename
        or die "Can't open $filename: $!\n";

    while ( <$fh> ) {
        next if not /ver = '(.*?)'/;
        $old_version = $1;
        last;
    }
}
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In which case $fh goes out of scope at the end of the block and the file is closed automatically; much nicer. I only explicitly close files that I write to (because they you want to check the return value of close, which may fail for such reasons as “disk full” or the like).

In fact, if the file is so small that you don’t mind slurping it, you could just say

use List::Util qw( first );

my $old_version = do {
    open my $fh, '<', $filename
        or die "Can't open $filename: $!\n";

    first { /ver = '(.*?)'/ } <$fh>;
};
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Makeshifts last the longest.