Opposition groups immediately filed petitions against the law, which in their opinion removes an important check on executive power.
Demonstrations took place again on Wednesday across the country.
Impacts the new law will have on the economy can already be seen.
Just one day after the vote, Morgan Stanley downgraded the country's credit rating.
Another rating agency, Moody's, warned of negative consequences for Israel's economy given the political and social tensions.
The Israeli currency, the shekel, also lost value.
Israeli President Benjamin Netanyahu and Finance Minister Bezalel Smotrich tried to appease the markets
"This is a temporary reaction; When the dust clears, it will be clear that the Israeli economy is very strong," they said in a statement.
Major businesses had warned several times in recent months that the reform could scare off investors and hurt the economy.
Companies in the high-tech sector announced they would withdraw funds.
The dynamic start-up scene is considered the most important driving force of the Israeli economy.
The controversial plans are also causing uncertainty on the street.
According to a recent survey by Channel 13, more than one in four citizens, or 28 per cent, are considering leaving the country.
In general, only 22 per cent of people are behind the government's plans, according to another poll by Channel 12.
The protest movement announced its intention to demonstrate "until the end".
Another large rally is planned for Saturday in Tel Aviv.
Actions in other parts of the country are also planned.
Israel's former prime minister Ehud Olmert has already warned of civil war if the government does not stop its plans.
The new law is also opposed by more than 10,000 reservists who say they will no longer report for duty, raising concerns that the military would no longer be ready for action in the event of an armed conflict.
Reservists make up a large part of the Israeli military.
Next week, the Defence Committee plans to hold a special session to discuss possible conscientious objections.
For weeks, there have been repeated incidents between Israel and the Hezbollah militia on the border with Lebanon and the political turmoil is seen as benefiting Israel's enemies.
"This is what is putting them on the path of collapse, fragmentation and disappearance, God willing," Hezbollah chief Hassan Nasrallah said of the developments in Israel.
On the official front, Israel's President Isaac Herzog said he had worked with all his might to reach a compromise on the controversial law and is "deeply disappointed" that it failed.
"I am also hurt and I am also angry," he wrote on Facebook on Wednesday.
But he said he was not ready to give up hope.
Herzog also said he was worried about the reservists, whom he called "the best of the best" and asked them to think about their pledge to not show up for duty, noting that Israel is their home.
It remains to be seen how the Israeli Supreme Court will act.
So far, no part of the Basic Law has ever been repealed in Israel, only regular laws that violate the Basic Law.
Israel has no constitution and is instead based on a collection of basic laws.
If the court were to oppose the government's law, this could lead to a kind of constitutional crisis as responsibilities would no longer be clearly defined.
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