American Rossi had been appointed as Caterham Formula 1 team's reserve driver alongside Ma at the start of last month.
On Wednesday, Caterham announced that Rossi will move to the GP2 squad for the remainder of the 2013 season, having missed the first race at Sepang.
He will retain his role as reserve for the F1 team alongside Heikki Kovalainen.
Chinese driver Ma, who finished 21st and last in his debut race, will stay involved with Caterham, but the team said his plans would be announced in due time.
Rossi last raced with Arden Caterham in the Formula Renault 3.5 series in 2012, when he finished the championship in 11th position.
He will race in GP2 alongside Spaniard Sergio Canamasas.