Sky Italia said Schumacher, a member of Ferrari's junior development academy, will drive the Ferrari on April 2 and the Alfa Romeo a day later.
The Alfa Romeo team have links to Ferrari, who signed Schumacher as an academy driver in January.
This came on the back of a successful campaign in the European Formula 3 championship past year, where Schumacher tallied eight wins to take the title.
It was also confirmed that he would have F1 test drives at Alfa Romeo the following day.
Michael Schumacher, 50, won five of his record seven titles with Ferrari.
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The 20-year-old will also be making his Formula 2 feeder series debut in Bahrain over the weekend and is delighted to be involved with his father's former team.
Ferrari locked out the front row in Bahrain previous year, with Sebastian Vettel going on to win the race following his triumph in the season-opener in Australia.
"I am obviously more than excited and would like to thank Ferrari for giving me this opportunity", Schumacher said in a statement. He secured eight wins from a total of 12 races and scored an invincible 347 points in the entire season. "The tests, often referred to as the 'Young Driver Tests", have previous of allowing younger talent to leave an impression in F1.
"We are therefore very pleased to be able to give Mick and Callum the opportunity to experience driving a Formula One auto".
The German, son of seven-time world champion Michael, has not driven a contemporary F1 auto before - but did try out a 1994 Benetton at Spa two years ago.