Polls indicate that the AfD could win an absolute majority in a state election in September in Saxony-Anhalt, meaning that it would form a state government for the first time.
Under Germany's federal system state governments have broad powers in many areas, including the activities of the police and intelligence services.
When asked by the Bild daily whether an AfD state government would have consequences for army bases in those states, Pistorius said: "We are looking very closely at the question of whom we can grant access to classified information.
"We are obliged to do so because it is about the security of our country."
Pistorius, who belongs to the centre-left Social Democrats (SPD), said he would feel uneasy passing classified information on to an AfD state minister.
"You only have to listen to the public statements of many, many AfD representatives. Their proximity to Putin is impossible to overlook," he said, referring to Russia's President Vladimir Putin.
The AfD is regularly criticised for close ties to Moscow.
Another state in the AfD's eastern heartland, Mecklenburg-Western Pomerania, will also hold an election in September.
There the party is also leading in the polls but is less likely to achieve an absolute majority.
Since coming second in last year's general election the AfD has been steadily climbing in national polls, with Chancellor Friedrich Merz's centre-right CDU/CSU slumping to second place.
A national poll published on Sunday gave the AfD an eight-point lead over the CDU/CSU, with the parties on 29 and 21 percent respectively.
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