"Israel is monitoring the situation in Iran very closely. We have eyes, ears and even more inside Iran," Yossi Cohen said during a closed session at the Finance Ministry, according to Israeli radio.
Cohen said the current unrest in Iran "was not likely to topple the regime at present."
"I would be very happy to see a social revolution in Iran. That's something that could perhaps happen in the future," he said.
Iran was hit by protests in late December over rising inflation, unemployment, and perceived government mismanagement.
The protests later seemed to turn into anti-regime rallies, spreading to several provinces, including capital Tehran.
More than 20 people were killed in the demonstrations, including at least one police officer, while more than 1,000 others were detained by authorities.