I can't find any documentation regarding this, take a look at..
https://support.microsoft.com/en-us/gp/framework_faq/en-us
.NET Framework 3.5 SP1: Beginning with .NET Framework 3.5 Service Pack 1 (SP1) the .NET Framework is defined as a component instead of an independent product. So, support for .NET Framework 3.5 SP1 is driven by the support lifecycle policy of the Windows operating system (i.e. when Windows is in the Mainstream Support phase or Extended Support phase, so are its components). When a product such as Windows reaches the end of support, so do its related components. .NET Framework 3.5 SP1 is supported on Windows Server 2003 SP2, Windows Vista SP2, Windows 7 SP1, Windows Server 2008 SP2, Windows Server 2008 R2 SP1, Windows 8.1 Update, Windows Server 2012, Windows Server 2012 R2, and Windows 10 according to the end of support date for each operating system.
Windows 2016 Server is not listed, but I have a feeling maybe the document isn't updated to reflect the new server OS? I know as I was able to add it as a "Feature" but it wasn't installed as part of the OS.
If anyone has any updated information regarding this, It will be beneficial to me and the community.
Yes, Net Framework 3.5 is working on Windows Server 2016, I have it installed on my Servers. So far, we haven't had any reported issues from our programmers.
Remember, You need to install it as a server feature. (Make sure to Specify an alternate source path during the installation. You need to mount your Windows 2016 Disk and set the path to Drive:\sources\sxs).
Microsoft has updated their FAQ
https://support.microsoft.com/en-us/help/17455/lifecycle-faq-net-framework