Gene, 30, has been employed in the same role with BMW-powered Williams for the past four years.
The 18-year-old completed 65 laps with a best time exactly three seconds slower than Ralf Schumacher.
Williams' German driver will make his return from injury in a three-day test at Monza next week.
The Formula One team will try out the sons of former champions Nelson Piquet and Keke Rosberg next week.
"It's better to be a Ferrari test driver than to drive for an uncompetitive team," the Spaniard said.
Formula One teams say they will race in Russia, despite the crisis in Ukraine and downing of a Malaysian airliner, unless the country's debut Grand Prix in October is called off or they are ordered not to go.
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