The country's number-two automaker said someone began hitting its sites on Tuesday evening.
"We take any potential threat to our information systems seriously," Nissan said in a statement.
"Because of a potential distributed denial of service attack, we are temporarily suspending service on our websites to prevent further risks."
An activist claiming to be associated with loose hacking collective Anonymous posted a message on Twitter saying "Japan stop the killing now".
The message was accompanied by pictures of a Nissan executive standing beside Abe, and images of what appeared to be dolphins being hunted, possibly by Japanese fishermen.
The rest of the Twitter feed contains objections to whale hunting.
Public broadcaster NHK said about 100 organisations across Japan were hit by cyber similar attacks in the last few months of 2015, including the official website of Prime Minister Shinzo Abe.
Japan regularly comes under fire for the annual hunt dolphin slaughter in a small town, which attracted global attention after it was featured in the Oscar-winning 2009 documentary "The Cove".
And in November, Tokyo sent a whaling fleet to the Antarctic for what it says is scientific research mission that will involve the killing of whales, despite a worldwide moratorium.
The move, which came after a one-year hiatus, angered activists and governments opposed to the hunts, including Australia and New Zealand.
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