You won't need mod_rewrite to do this, hope this should do the trick:
SetEnvIfNoCase Request_URI ^/some/path/to/protect require_auth=true
SetEnvIfNoCase Request_URI ^/another/protected/path require_auth=true
AuthUserFile /var/www/htpasswd
AuthName "Password Protected"
AuthType Basic
Order Deny,Allow
Deny from all
Satisfy any
Require valid-user
Allow from env=!require_auth
mod_auth mod_env mod_rewrite, . SetEnvIfNoCase Request_URI ^/some/path/to/protect require_auth=true , auth .