The game in the city, 310km to the north of Buenos Aires, was already scheduled to be played behind closed doors, but that didn't prevent violent incidents on the streets around the ground.
"It's been suspended," said Central president Norberto Speciale.
The match between the two most popular clubs in Rosario was preceded by a series of incidents involving arson attacks on commercial premises. Some 800 police were deployed around the Rosario ground.
Rosario Central and Newell's were due to play the first of two friendlies with the matches taking on greater significance as the clubs play in different divisions of the Argentine championship.