Can I use perl's switches with /bin/env in the shebang line?

I want to run perl -w using env. That works fine on the command line:

$ /bin/env perl -we 'print "Hello, world!\n"'
Hello, world!

But it doesn't work on the shebang line in a script:

#!/bin/env perl -w
print "Hello, world!\n";

Here is the error:

/bin/env: perl -w: No such file or directory

Apparently env doesn't understand the -w flag that I'm passing to perl. What's wrong?