I managed to get it working using the below apache config. However, it works only if username and password is simple. If password is complex, the passthrough feature does not work and I have to re-login in RMQ management UI too. So I'm checking how to overcome that - any help is appreciated, thanks:
#get authorization, format it and assign it to cookie in rmq-ui compatible format
RewriteCond %{HTTP:Authorization} "^Basic (.*)$"
RewriteRule .* - [E=authcheck:%1,NS]
Header set Set-Cookie "m=2258:%{authcheck}e"
AllowEncodedSlashes On
<Location /rabbitmq>
ProxyPass http://RMQNODE:15672 nocanon
ProxyPassReverse http://RMQNODE:15672
ProxyPassReverseCookiePath / /rabbitmq/
</Location>