The team admitted last night that their final day plans were in jeopardy - and following a thorough overnight inspection they have formally confirmed their withdrawal on safety grounds.
The team say they will use the day to prepare a second chassis at the circuit, as they bid to be ready for the start of the second and final test on Tuesday March 7.
"Following a thorough inspection overnight some damage to the FW40 chassis was discovered and therefore, on safety grounds, the team will not run the car today," Williams said in a statement.
"A second chassis will be prepared at track this afternoon, as originally planned, with the team aiming to be back on track for the second test next week."
The first half of day four will be dedicated to wet-weather running, with Pirelli having soaked the circuit overnight in order to allow teams to trial the new wet and intermediate tyres.