The 26-year-old, who tested in 2001 for Jaguar and Jordan, will drive Minardi's PS03 chassis on Friday at the Vallelunga circuit near Rome.
"This is clearly a great opportunity for me," he said in a statement released by Minardi.
"It will be great publicity for India and for Indian motor sport," added Karthikeyan, who was fourth in the 2003 World Series.
Minardi team principal Paul
"Narain is undoubtedly the most talented driver from India currently on the international motor racing scene, showing tremendous commitment every time he is behind the wheel. We believe he has great potential."
The statement said that if the session went well, there was a strong possibility Karthikeyan could be asked to join the team in 2004.
One of Karthikeyan's sponsors, however, said his chances would also depend a lot on his ability to raise money from sponsors for the cash-strapped team.