Note, however, that -- as originally posted --your regex does NOT match (has a typo?).

#!/usr/bin/perl -lw
use strict;
# [id://735593]

my $string = '<img id="image-1" src="http://site.com/a.gif" />';
my $regex = qr|<img id="image-(\d)" src="http://site.com/(\w\.\w+)" />
+|;    # works
#                                                         ^^^^^^^     
+      < modified here
if ( $string =~ /$regex/ ) {
  print "\$regex matches: $1 and $2";
} else {
  print "No match in $regex";
}

my $OPregex= qr|<img id="image-(\d*) src="http://site.com/(\w*)" />|; 
+    # OP's with (added) terminating "|;"
if ( $string =~ /$OPregex/ ) {
  print "\$OPRegex matches: $1 and $2";
} else {
  print "no match in \$OPRegex";
}
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Output:

perl  F:\_wo\pl_test\735593.pl
$regex matches: 1 and a.gif
no match in $OPRegex
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