You'd think that you could import this using vSphere Client, but the VM has to be converted first using the (free but registration required) VMware Vcenter Converter Standalone. I downloaded version 5.1 and installed it.
This is the screen that I got when first starting it.
I selected convert machine (top right). In the Conversion dialog, I selected source type as "VMware Workstation or other VMware virtual machine" and the source as the *.vmx file.
Then I selected the destination type as "VMware Infrastructure virtual machine" and put in my server details.
I hit next, and the converter connected to the ESXi server. This is where I could assign a new name to the VM. I left it as Metasploitable.
The next screen asked which datastore to use for VM and what VM version to make it. I left the defaults. The next screen listed some options (disk, cpu, network, etc.) that could be changed. I left them as is and hit next. The last screen was a summary/confirmation screen. The converter submitted the job after I clicked "finish."
Here is what the job looked like.
It quickly changed from one hour to six minutes. The new machine showed up in vSphere Client right away.