We are running a Active / Active DataCenter with Stretched ESX Cluster. If a VM moves from DC 1 to DC 2, what is a possible method of injecting a specific Route for that Particular VM. Since the Application running on the VM, is not behind a Load Balancer, we cannot use Route Health Injection.
I think the options you have will depend upon the platforms you're using, and what your requirements are with respect to scale and automation.
If you want a solution where you're moving 100/1000s of VMs on a regular basis, and you want these to be simply moved with little or no co-ordination between the server and network teams, then LISP (Locator / ID Separation Protocol) is probably the direction to start looking.
If you only have a small number of VMs moving at any point in time, and you're quite happy with the server team being able to deliver a list of VMs IP addresses to the network team, then a very simple solution is redistribution of static host routes into your IGP. The exact mechanism may vary depending upon the platform, but essentially you add one or more static host routes (the IP of the VMs being moved) on the LAN routers in DC 2, and redistribute these into your IGP. You also need to add proxy ARP to the routed interfaces for the VLANs in both DC1 and DC2 so that hosts within the same VLAN can still communicate.
It's not the most scalable solution as there's obviously management overhead for the server and network teams each time a host moves, but it does work and involves no real engineering effort to test and certify a solution such as LISP.
If you're running Catalyst 6500 you can inject host routes in a slightly more automated manner using Cisco Local Area Mobility, but note that this feature has limited platform support and my guess is that it won't be around for too much longer.