The graduates were seen driving a convoy of black Mercedes jeeps noisily through Moscow last month, blocking traffic and hanging out of the windows.
Some veteran Russian spies have said such behaviour amounted to treason.
The FSB says those involved will have the conditions of their service changed, without elaborating further.
In a statement (in Russian), it also says some of the FSB Academy's senior officers have already been demoted and some will be sacked.
"The immodest, demonstrative behaviour linked to the short-term rentals from a luxury car company sparked justified indignation among citizens and strong condemnation from the community of military security bodies."
Footage of the celebration was posted online shortly after the incident, attracting hundreds of thousands of viewers.
The FSB is the main successor of the Soviet KGB.
The agency's powers and budget have risen significantly under President Vladimir Putin - himself a former KGB officer.
Russia's FSB security service says it will punish a group of new agents who allowed themselves to be photographed lavishly celebrating their graduation.