Is there a better way to do this?

A better way, in my opinion, would be to have the return value of routine indicate whether the for loop should move onto the next value.

foreach $row (@array) {
  next unless routine($row);
  # more code here
}

sub routine {
  if ($row != '10') {
    print "stuff";
    return 1;
  } else {
    return 0;
  }    
}
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A minor issue with your code as posted: You cannot say $row != '10'. You are using numeric equality against a string. The correct technique is to either compare against a number $row != 10 or compare using string equality $row ne '10'.

You can get Perl to help you with looking out for problems like this if you have warnings switched on. To enable them, add a use warnings; somewhere in the file.