Police found over a dozen bullet casings at the station, along with a makeshift bomb that failed to explode.
Alter is operated by a publisher who also owns a newspaper hit in arson attacks last week, which a group called "Conspiracy of Fire Nuclei" claimed responsibility for.
Police said they have matched bullet casings from Tuesday's attack to weapons used in a similar attack against an Athens police station two weeks ago.
A group called "Sect of Revolutionaries" claimed responsibility for the attack, and have said they will expand their targets to include journalists and politicians.
Athens has been hit by a spate of attacks from left-wing extremists in the past two months, with the majority aimed at police stations.