RPi 3 reboots every 5 minutes after upgrade to Ubuntu MATE 16.04.1

Hello, welcome!

The Raspberry Pi version isn't supposed to be upgraded. The kernel is different to that of the desktop edition and the upgrade has left your Pi running the 15.10 kernel instead of the one used in 16.04).

You could try manually updating the kernel:

sudo rpi-update

Really, it's not recommended to upgrade the Raspberry Pi version across release versions as mentioned here: