The prince, Saudi Arabia's de facto ruler, has taken a hard line on Iran.
He told the New York Times it could not be allowed to spread its influence.
"We learned from Europe that appeasement doesn't work. We don't want the new Hitler in Iran to repeat what happened in Europe in the Middle East," he said, referring to Ayatollah Ali Khamenei.
His remarks drew a strong response from Tehran.
Iranian foreign ministry spokesman Bahram Qasemi accused the "adventurist" crown prince of "immature, inconsiderate, and baseless remarks and behaviour", the semi-official Isna news agency reported.
"I strongly advise him to think and ponder upon the fate of the famous dictators of the region in the past few years now that he is thinking of considering their policies and behaviour as a role model," he said.
Relations between the two powers have become increasingly strained.
Earlier this month, the prince blamed Iran for a missile attack aimed at the Saudi capital, Riyadh, by rebels in neighbouring Yemen. He said the attack might be considered an act of war.
Iran denied it was involved.
Sunni-Muslim majority Saudi Arabia and Shia Muslim-led Iran are at loggerheads across the Middle East.
The Saudis accuse Iran of helping Shia Houthi rebels in Yemen, where a Saudi-led coalition has been fighting a war since 2015.
Iran and the rebels deny the charge.
Saudi Arabia has been widely blamed for exacerbating Yemen's humanitarian crisis by imposing a blockade on the country.
Saudi Arabia has also warned against Iran's growing influence in Iraq, where its proxy militias have played a key role in defeating so-called Islamic State, and in Syria, where it has militarily helped President Bashar al-Assad gain the upper hand in the civil war.
Both countries have also accused one another of trying to destabilise Lebanon, where the pro-Saudi prime minister leads a coalition including the Iranian-backed Hezbollah movement.
The prime minister, Saad Hariri, recently announced - then suspended - his resignation, accusing Iran and Hezbollah of sowing strife, while Iran accused Saudi Arabia of engineering the crisis.
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