The move is a response to the increasingly tight restrictions in place in Italy in the light of the coronavirus outbreak.
The wet weather test was supposed to be the second of 25 'mule car' days scheduled for 2020 and shared between the 10 teams, following a session with Ferrari and Charles Leclerc at Jerez earlier this month.
It was also the only opportunity for any F1 car to run between the end of Barcelona testing last Friday and first practice in Australia.
The tyre company said on Twitter: "Because of company restriction policies adopted by Scuderia Ferrari and Pirelli following the worldwide Coronavirus outbreak, the scheduled 18-inch 2021 wet tyre test at Fiorano on March 5 has to be postponed.
"The test will be rescheduled at Fiorano at the earliest opportunity."
Bahrain GP organisers have contacted teams, media and others travelling to the race and asked them to clarify whether personnel will have been in or passed through affected countries in the 14 days prior to their arrival, as part of a wider plan to address potential travel issues.
The list of countries includes Italy, Japan, China (including Hong Kong), Iran, Iraq, South Korea, Malaysia, Singapore, Egypt, Lebanon and Thailand.
Personnel are also asked to declare if they intend to transit through Dubai on the way to Bahrain. Emirates is one of the few airline options for the trip from Melbourne, but in recent days Dubai/Bahrain flights have been subject to restrictions.
The race organisers noted: "Bahrain International Circuit is working with Bahrain's Ministry of Interior and Ministry of Health to put in place specific measures for teams, administrators, broadcast and media attending the upcoming F1 Gulf Air Bahrain Grand Prix."
On Monday, Vietnam announced that it was suspending visa-free travel for Italians.