"The attack did not succeed on the scale that had been planned," he said, adding that "a lot indicates that (it) took place from the territory of Iran".
"There was an attempt to breach security, which was stopped," Gawkowski told a podcast for rolling news channel TVN24+.
While Gawkowski said that he could not reveal when exactly the attack to place, he said it had been within "the last few days".
He said security services in the NATO member had been on high alert since the war in the Middle East broke out.
"Incidents have emerged that may be connected to adversaries from that part of the world," he said.
The minister said "the places from which" the nuclear centre near the central city of Otwock "was attacked are linked to Iran".
But Gawkowski warned that "this may be a kind of camouflage" and that further investigation was going on.
"When there is final information and the (security) services have checked everything, we will verify it," he said.
The debate over nuclear weapons has heightened in Poland, an EU member that borders Russia, Ukraine and Belarus, since the beginning of the Iran conflict and amid the ongoing war in neighbouring Ukraine.
Conservative-nationalist President Karol Nawrocki has said Poland should "begin work" on nuclear defences, while centrist Prime Minister Donald Tusk has said Warsaw "is talking seriously" with Paris about being protected by France's nuclear umbrella.