The Mudcat Cafe (mudcat.org) offers the following insight about this common sea shanty phrase.
When you are on the deck of a ship (sailing or otherwise) and a solid wave of water (continental or deep ocean) comes over and completely submerges you, all you can see is green — Ted
Shipping it green just means that the wave that breaks over the ship is deep enough at deck level to be a solid wall of water, unbroken, not surf. — Robin