The group of teenagers arrested included at least three Albanians, seven Greeks and five Italians.
"Five Italians and seven Greeks have been arrested, while dozens have been detained," a police official said.
"Some were throwing stones at police and others were armed with wooden sticks."
Several protests are set to take place across Greece on Sunday to mark the anniversary of the shooting.
The demonstrations are expected to include a march through the capital as well as a memorial service at a makeshift shrine in central Athens on Sunday.
A gathering is also planned at the scene of Grigoropoulos's shooting in Exarchia district.
Greece's government has deployed at least 6,000 police onto the streets of Athens to avert a repeat of the severe rioting that hit the capital and major cities last year which caused millions of dollars of damage.
Greece's government also said it will not tolerate a repeat of last year's riots while Karolos Papoulias, the president of Greece, had pleaded for calm ahead of the planned protests.
"The murder of Alexis Grigoropoulos was not only a heinous act, it was a lesson for us all ... an obligation to try and ensure a fairer society for our younger generation," he said.
Theodoros Pangalos, the Greek deputy prime minister, said:"We will not tolerate lawlessness and attacks on innocent citizens."
Grigoropoulos was shot dead by a police officer who claimed he fired into the air whilst under attack by youths, but the death has managed to spark weeks of violence across Greece.
Two police officers have been charged with murder and attempted murder for the teenager's death and are scheduled to stand trial on January 20.
Fears of violence have been heightened by reports that groups of anarchists from other European countries are planning to join the protests in Athens.