open FILE, "/path/to/file" or die "$!\n";
open OUT, "/tmp/tmpfile.$$" or die "$!\n";
while(<FILE>) {
  next if /^\s*$/;
  print OUT, $_;
}
close FILE; close OUT;
rename("/path/to/file", "/path/to/file.bak")
  or die "Error in rename: $!\n";
rename("/tmp/tmpfile.$$", "/path/to/file")
  or die "Error in rename: $!";