The bottles matter more than the racks, so pack them first into proper divided wine boxes rather than leaving them in place while you disassemble the shelving around them. Once the bottles are safely packed, most modular racking systems come apart like a large bookshelf kit.
Pro tip: Photograph any handwritten cellar inventory or tasting notes before the move, since a scattered collection reshelved out of order is much easier to sort with a reference list.
Watch out: Never lay bottles on their side loosely in a standard box; use dividers and keep them upright for the move, since sustained side pressure combined with jostling stresses corks more than upright transport.