Xen is a hypervisor with a bare microkernel on which VMs (windoze, linux, etc.) run. It dosen't need Linux or other OS-es to run.
To "embed" it in Linux is kind of a nonsense, as Linux is (one of) the VM(s).
KVM is actually Linux with hypervisor functionality included, on which other VMs can run.
More Linux Distributions are jumping on the KVM bandwagon, including Ubuntu, for virtualisation.
footnote: Linux is actually the kernel. The term is misused often to name a Linux Distribution or the OS ( = Linux + system utilities and libraries, aka GNU) which is correctly named Linux/GNU.
@Human think: you're welcome
A further clarification:
To fully support the other VMs (domU), on Xen runs a privileged VM (dom0) which provides the interface services with the real HW, which the microkernel doesn't include.
While initially Xen supported just Linux/GNU with a special kernel, there is also support for other OS-es as dom0.