The detention centres have reportedly become targets of intimidation attempts, ranging from cars set on fire to shots fired with automatic weapons.
Darmanin planned to visit an affected prison in Toulon in southern France on Tuesday afternoon.
There were no reports of injuries.
The minister views the overnight attacks as a co-ordinated response from organised drug crime, against which France has declared a fight on various fronts.
Prisons in Marseille, Valence, Aix-en-Provence, Nîmes, Nanterre and Villepinte were also affected by the attacks, the newspaper Le Parisien reported citing the Justice Ministry.
The anti-terrorism prosecutor's office has reportedly been tasked with the investigation.
Interior Minister Bruno Retailleau described the incidents as "unacceptable attacks on the staff and property of the penal authorities".
Several cars belonging to pupils of the training academy for judicial employees in Agen were set on fire for the second time on Monday night.
The justice minister recently announced the construction of a high-security prison where all convicted serious drug criminals in France are to be housed.
This is intended to put an end to the practice of serious criminals having access to mobile phones behind bars despite a ban, allowing them to continue co-ordinating their operations, including contract killings, from their cells.
Additionally, a law is being developed in France to enable a tougher crackdown on drug trafficking.
## Update -
## Note to editors - dpa photos
## Internet links - [Interior minister's statement, in French](https://dpaq.de/hWTovzy) - [Justice minister's statement, in French](https://dpaq.de/NqrEr2i) - [Le Parisien report, in French](https://dpaq.de/PU8dUEG) - [France Info report, in French](https://dpaq.de/iAq7vU5)
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