Yes it is, WE went on a cruise for our honeymoon and it was great. Once you get on ship and get unpacked, all the action comes to you.
First you need to pick a good cruise itinerary so you get to see and do things that the two of you like. If you want sun and the beach, do a caribbean cruise. If you are into historical stuff, do a Mediterranian cruise.
Almost all cruie lines have the same setup, but Carnival is for the younger crowds (i.e., 20's to 30's). I would stay away from Disney, too many kids. Try Royal Caribbean or Princess. Norwegian is good, but they don't have the personal service that others do with their "freestyle" cruising.
When you book, ask for a table for two so you and the bride can have some privacy at dinner. You will meet plenty of people other times. Cruises have entertainment on ship and great tours to keep you busy all day. Also, book a balcony cabin, its worth the extra money to have a place where the two of you can be outside in privacy. Make sure that you let them know when you book that its a honeymoon, They will do special things. On Princess they decorated our cabin door with baloons. They will have a get together for all the honeymooners and aniversary people.