You don't need the .replace() code (it also only works on strings); PHP can already do the proper conversion for you:
$(function() {
var amount_min = <?php echo isset($_GET['amount_min']) ? (int)$_GET['amount_min'] : 0; ?>;
$('input[name=amount]').val(amount_min);
});
You could also use filtering for this:
<?php echo filter_input(INPUT_GET, 'amount_min', FILTER_VALIDATE_INT, array('options' => array('default' => 0))); ?>
Note that filter_input would not accept a value like 100abc, so use wisely.
If you still want to use strings safely in JavaScript you should use json_encode().
Btw, any answer that involves an unmodified echo of a request variable from PHP inside JavaScript code is wrong and can cause XSS attacks! You have been warned.
Update
The regular expression based replacement can also be done in PHP:
var amount_min = <?php echo (int)preg_replace('/\D+/', '', isset($_GET['amount_min']) ? $_GET['amount_min'] : 0); ?>;
Since all non-digits are removed, you can safely apply the (int) cast.
.replace()function for numbers in JavaScript.