If you watch your connections and make no nasty groundloops you should be fine.
If we imagine that your pot is connected to the VFD with three pins and one of them is ground, this is how i would do it:
Power the Arduino from a seperate power supply (USB "charger" is handy)
The inputs on the typical Arduino can not tolerate more than 5V maximum, so we need to halve the 0-10V signal.
You need a voltage divider that's 10 times higher in resistance than the pot to not affect the pot too much.
e.g. with a 10K pot on the VFD, make a voltage divider with two 100k resistors and feed the midpoint of it to analog-in on the Arduino.
// Per.