Accepted Solutions
Is the Static IP Address being assigned in the same Subnet as the NAT Network, default VMnet8, and outside the Scope of the VMnet's DHCP IP Address Pool?
See 
DHCP Conventions for Assigning IP Addresses in Host-Only and NAT Networks for example.
Otherwise...
VMware Product and Version?
Host OS Product and Version?
What VMnet is being used for NAT Networking, the default VMnet8?
How is the Host connected to the Internet, Wired Ethernet or WiFi?
In a Command Prompt, output of ipconfig /all on Windows Host and or Guest.
In a Terminal, output of ifconfig -a on Linux Host and or Guest.
If the information you've presented is correct then here is the issue I see:
The Host's IP Address and the VMnet Address are on the same Subnet and this normally should't be! Because the Host's VMnet Network Adapters IP Address is by default .1 on the last octet and you said the VMnet's IP Address Subnet is 192.168.1.0, thus making the the Host's VMnet Network Adapters IP Address 192.168.1.1 which is the same at the Host's Gateway IP Address of 192.168.1.1. Normally the only way the VMnet's IP Address Subnet would be the same as the Host's IP Address Subnet is if the User modified the VMnet's IP Address Subnet manually in the Virtual Network Editor as VMware Workstation would not have configured the VMnet to use the same Subnet as the Host's! 
This is also why I asked for the output of ipconfig /all (or as applicable, ifconfig -a) on Host and Guest as it actually provides a bit more diagnostic information then you provided. I much prefer seeing copied/pasted command output then human translated information as it to easy to make typos!
Anyway since you didn't actually provide all the information requested I cannot comment based on all the technical facts however while it might be working at the moment nonetheless you best make sure you have things properly configured so it continues to work. Based on the information you provided, things are not properly configured!