Are RF shields necessary?
In the United States the FCC (Federal Communications Commission) Part 15 regulates unlicensed transmissions.  

It doesn't matter whether you are using a "module", it is the unlicensed use of any transmission.  

The FCC doesn't care HOW you comply with the regulations. If a device complies with regulations without using a shield, so much the better.   

Fair article regarding FCC Part 15

(Shield meaning here is a metal envelope or enclosure, not shield as used in Arduino definitions)   

EDIT 1 :  A device manufacturer might also use shielding to make their product more immune to interference from other electro-magnetic interference.  

EDIT 2 :  After seeing comment by DigitalNinja, I did further research. Apparently the FCC does use the terminology "module" and "modular". The following is extracted from : October 23, 2015 TRANSMITTER MODULE EQUIPMENT AUTHORIZATION GUIDE  :  

One definition of modular is cited, among many other types of modular as,  


  Single-modular transmitter is a self-contained physically delineated component that can demonstrate compliance independent of the host operating conditions, and complies with all eight requirements of the Section 15.212(a)(1) and summarized below.  


Further quoting,


  and which complies with all eight requirements
  of § 15.212(a)(1).   


Which includes as the first item :  


  1) The radio elements must have the radio frequency circuitry shielded. Physical components and tuning
  capacitor(s) may be located external to the shield, but must be on the module assembly;
  2) The module must have buffered modulation/data inputs to ensure that the device will comply with Part 15
  requirements with any type of input signal;  


There are other sections of the same "Authorization Guide" that allow compliance with the FCC Guide without using shields.  Often regulations can conflict with themselves. I can now see where the original OP,  and the commentor DigitalNinja have concluded a shield is necessary, even though I read the FCC guide as not requiring a shield, or perhaps the definition of a "shield".