The measures are described as part of an investigation into a suspected plan to incite riots and destabilize the country in connection with the upcoming parliamentary election.
The police state that it is a plot that "has been coordinated from Russia, through criminal elements".
The total of 74 people arrested have been detained for up to 72 hours, says prosecutor Victor Furtuna.
The election on Sunday is seen by many as a choice between a continued course towards EU membership, or towards a rapprochement with Russia.
Moldovan authorities have long accused Russia of interfering in the country's elections through disinformation and financing of pro-Russian parties.
Moscow has dismissed the allegations.
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