Not in general.  It might fall under one of the NECs "tap rules" in some situations for short runs, subject to approval of local AHJ.  Feeder to the VFD needs to have its own circuit protection upstream at the source end.  

Even if the VFD was close enough to fall under a tap rule, a VFD is considered a motor controller.  All motor controllers must have an individual disconnecting means (except in one specific circumstance) within sight of the controller so you would still need at least a switch, so you might as well put the circuit protection in .  I agree with dpc.  

Was there a specific situation you were thinking about?  I can't think of a situation where you would not want to put in overcurent protection.

The single line is described as follows,

Source-4160V,
Fuse-disconnect(including an isolation switch and fuse)which can provide overcurrent protection against fault,
Contactors are located upstream of VFD,

VFD is the only downstream drive before the motor, not other tap circuit.  
 

I was thinking low voltage (<600V), not medium voltage.  The fuse should be providing overcurrent protection for the MV feeder cable also.  What kind of fuse are you using, E or R?  Also for a controller over 600V the disconnecting means is not required to be within sight as long as it can be locked open.  If you are using an E fuse you should be good to go.  If you are using an R fuse I would just change to an E fuse.  You really don't need its characteristics with a VFD.

We are using E fuses. The fuse can't provide overload protection to cables, only overcurrent protection.

Per 2005 NEC for MV Feeders:

240.101 Additional Requirements for Feeders.

(A) Rating or Setting of Overcurrent Protective Devices. The continuous ampere rating of a fuse shall not exceed three times the ampacity of the conductors.

Per Littelfuse:

“E” rated fuses are considered to be general purpose fuses and can be
used to protect against low and high values of fault current. “R” rated
fuses are designed for back-up protection. They must be used in series
with other devices such as motor overload relays in order to achieve
both overload and short-circuit protection.
Medium voltage fuses are not intended to provide overload protection in
the same sense as fuses rated 600 volts or less. Medium voltage fuse
current ratings do not have the same meanings as the ampere ratings of
low voltage fuses.
All medium voltage fuses are limited in their ability to interrupt low value
overcurrents, especially those between 100% and 200% of the fuse’s
continuous current rating. They are designed to carry their rated current
without exceeding the temperature rise permitted by NEMA and ANSI
standards.
Application Note:
Since these fuses are used for the protection of general purpose
circuits which may contain transformers, motors, and other equipment
producing in-rush and/or overload currents, fuses should generally be
rated at 140% of the normal
full load current, and circuits should be
analyzed to ensure that system load currents will not exceed the current
rating of the fuse.

I have seen E fuses used to protect MV feeders.  I think that the intent of the code is probably what I now realize you were alluding to in your original question.  If there is an overload of the MV circuit then the protective device for the motor or transformer will interrupt the circuit.  If there is any type of fault, at that voltage it will easily exceed the 200% rating of the fuse and cause it to open.