The VirtualBox Packer builder is able to create VirtualBox virtual machines and export them in the OVA or OVF format.
Packer actually comes with multiple builders able to create VirtualBox machines, depending on the strategy you want to use to build the image. Packer supports the following VirtualBox builders:
virtualbox-iso - Starts from an ISO file, creates a brand new VirtualBox VM, installs an OS, provisions software within the OS, then exports that machine to create an image. This is best for people who want to start from scratch.
virtualbox-ovf - This builder imports an existing OVF/OVA file, runs provisioners on top of that VM, and exports that machine to create an image. This is best if you have an existing VirtualBox VM export you want to use as the source. As an additional benefit, you can feed the artifact of this builder back into itself to iterate on a machine.
virtualbox-vm - This builder uses an existing VM to run defined provisioners on top of that VM, and optionally creates a snapshot to save the changes applied from the provisioners. In addition the builder is able to export that machine to create an image. The builder is able to attach to a defined snapshot as a starting point, which could be defined statically or dynamically via a variable.