His Williams team said on Monday that Canadian Lance Stroll would drive on Tuesday instead, with young Italian Luca Ghiotto making his Formula One test debut as previously scheduled on Wednesday.
Massa, who felt dizzy in practice last Friday and Saturday, was replaced at the weekend by the team's experienced British reserve driver Paul di Resta.
The Brazilian is expected to return for the Belgian Grand Prix at the end of August, although there are no certainties.
"I think we're optimistic. It would be really a great shame if he wasn't ready for Spa," team technical head Paddy Lowe said at the weekend. "That's four weeks away so he ought to be in good shape by then."
While the test is mainly aimed at giving young drivers track time and, in some cases, a first taste of Formula One, the main media focus at the Hungaroring will be on Renault and the comeback of Robert Kubica.
The 32-year-old Pole, a grand prix winner with BMW Sauber in 2008, will be driving a contemporary Formula One car for the first time after impressing in previous tests in older machinery and on the team's simulator.
Kubica could be in the frame to replace Britain's under-performing Jolyon Palmer at Renault in what would be a remarkable return for a driver whose F1 career appeared over after a near-fatal accident in 2011.
The Pole partially severed a forearm when he crashed a rally car in a low-key event in north-western Italy that he had entered for fun before the start of that year's Formula One season.
Renault Sport F1 head Cyril Abiteboul said before the Hungarian Grand Prix weekend that Kubica was not an immediate threat to Palmer but the team were considering their options for next season.
"What we are doing with Robert has nothing to do with what Jo does this weekend or even after the summer break," the Frenchman had told motorsport.com.
"Jo will be driving in Spa, and the plan is for him to drive until the end of the season."
However, he also said he expected Palmer to score his first points of the season -- something the Briton failed to do. He is now one of just two drivers on the grid without a point after 11 races.
(Reporting by Alan Baldwin, editing by Nick Mulvenney)
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