That is because it is not evaluating that code and it is expecting a literal date value. Try using:
Min Date: <?php echo(date("m/d/y")); ?>
although that may not work either. Does the MinDate field have a lighning bolt next to it? If not it may not work with server code by default in that field. No worries, you should be able to update the code directly.
After applying look for the line of code where your minvalue is set and post it here. I can see if the syntax looks correct and advise you on changes.