The Williams FW13B contested the 1990 season, with drivers Thierry Boutsen and Riccardo Patrese collecting respective victories at the Hungarian and San Marino Grands Prix.
Massa will use it to tackle the famous UK hillclimb course on Saturday June 27, with Williams tester Alex Lynn doing the same the following day.
The FW13B in question got a warm-up outing on Tuesday with former F1 driver Karun Chandhok in the cockpit. It was the first run for the car - now part of the Williams Heritage collection - in 25 years.
Williams will have their current FW37 on display at Goodwood too, with many of their rival F1 teams also expected to be in attendance over the course of the four-day event, which starts on June 25.