The 23-year-old Japanese is currently a test and development driver with Honda-powered McLaren, focussing on work in the simulator.
Sauber are due to switch to Honda power next season, although that deal has been thrown into doubt by recent management changes at the team and reports that no final contract was signed.
Matsushita also competes in the Formula Two support series for the ART team, which is run by newly-appointed Sauber principal Frederic Vasseur.
"I am pleased that Nobuharu has this great opportunity. He deserves the experience of his first test in a Formula One car," said the Frenchman Vasseur in a team statement.
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"Ever since his debut in Formula Two with ART Grand Prix, I have been following his progress closely, and have watched him advance his performance from year to year.
"With this Formula One test, he comes one step closer to his dream of becoming an F1 driver one day."
(Reporting by Alan Baldwin, editing by Ian Chadband)
