From the very beginnings of object-oriented development, OO design has been linked with iterative and incremental development. But as many point out, there's no inherent link between the two. You can do OO in a waterfall, and you can do IID without objects. So why are the two so closely linked?
I don't think there's a definitive reason, but there are few indicators. One is a technical aspect. Objects provide a very fine grained modularity, where the program is divided into small substitutable modules with separation of interface and implementation. The class provides the encapsulation that supports the interface/implementation division and polymorphism provides a simple substitution mechanism.
This fine-grained modularity, when done well, allows you to make changes to an existing code base much more easily. This is important for IID because the whole point of IID is that you don't have a comprehensive design at the beginning, you grow the design and the code together. Good modularity is essential to this. (An interesting non OO example of this is the Unix community, which stresses modularity in order to evolve, but isn't so keen on OO.)
A large part of the impetus in the OO world comes from Smalltalk, even though the number of Smalltalkers are (and were) small, they were disproportionately loud. Smalltalk is an environment that has many features, beyond just the OO ones, that support IID. Immediate compiles and links into a running system, a good IDE that really helps navigate around the source code, emphasis on a graphical user interface (before this was common), an environment that hides many low level issues like memory management, a large class library - all of these things enable iteration. (Again the Lisp community also had all of this and is also strongly iterative.)
So there's technical reasons why objects encourage IID, but also there's social reasons. The leaders of the OO world pushed IID right from the beginning, which is why it's no surprise that the leaders of the agile movement almost entirely are OO people. When the leadership embraces both movements so fervently that has an effect on the whole community. I certainly grew up in this community with both objects and iteration as given.
All this doesn't mean that objects and IID are mutually necessary, but I think it does indicate why the two have such a strong affinity.