The law aims to combat the boycott, divestment and sanctions movement that urges companies, organisations and academic institutions to boycott Israel over its policies on the Palestinians.
Boycott activists have condemned the law as anti-democratic, but supporters say it is a necessary response to threats against Israel's legitimacy.
On the same day United States president Donald Trump issued his revised travel ban in that country, the closest US ally in the Middle East introduced its own ban.
The Israeli parliament approved legislation to deny visas to foreign nationals who issue public calls to boycott Israel.
The move is aimed at combatting the so-called BDS, boycott, divestment and sanctions, movement.
The movement encourages supporters of the Palestinians to pressure companies and organisations to boycott Israel over its policies towards the Palestinians.
The BDS has been growing in popularity in Europe and the United States.
The executive director of the US Campaign for Palestinian Rights, Yousef Munayyer, says the law shows the Israeli government is becoming increasingly concerned.
"In the past, what we used to hear from the Israelis is that Israel's enemies were all violent, those people who criticise the Israeli state are terrorists, and so on and so forth. But, now, we're seeing the state really cracking down and acting out against people who have embraced nonviolence."
It is not clear how Israel plans to use the new law or how many people will be banned.
In Australia, the Department of Foreign Affairs and Trade says it has not received any request for consular assistance relating to the ban.
Israel has blocked some activists from entering in the past, but there are concerns the new law could be used more broadly.
It targets those who make a public call for a boycott, which could, for example, include social-media posts.
Australia/Israel and Jewish Affairs Council executive director Colin Rubenstein says changes resulting from the new law will only be modest.
Dr Rubenstein suggests it is a symbolic reinforcement of current Israeli policy.
"What it's designed to do, of course, is to send a message to those people out to do Israel harm, or part of the international campaign which is well known to de-legitimise Israel. And, indeed, the Boycott Divestment Sanctions campaign is an important part of that international strategy to demean, defame and, essentially, to de-legitimise Israel."
Dr Rubenstein says every country is entitled to control who enters.
He says the ban was not targeted at limiting free speech nor legitimate criticism of the Israeli government.
"The efforts to undermine Israel have diversified from war to terrorism and, essentially, to a collection of activities that can be referred to as 'lawfare,' using a variety of techniques to try to undermine and de-legitimise and isolate Israel. And which Israel, as a society and certainly as a government, has absolutely woken up to in recent years and is determined to try and sidetrack, to contain and to, ultimately, defeat."
Australian Jewish Democratic Society executive member Jordy Silverstein is one of those who could be banned.
Her organisation advocates boycotting products manufactured in Israeli settlements on Palestinian territory.
Dr Silverstein has been to Israel previously and plans to go again in May on a tour organised by an international Jewish organisation.
She says the ban is undemocratic and the law's ability to block Jewish activists from Israel has concerned many in the Australian Jewish community.
"I think there are a lot of people who have really still clung to an idea of Israel as a Jewish home for all Jews. And I think those people are feeling really challenged, and that's kind of been the Jewish response that I've seen on Twitter and Facebook and online and in conversations since this law came into effect."
Israel's travel ban began on the same day President Trump signed his revised ban blocking nationals of six Muslim-majority nations from entering the United States.
But Australian National University international-relations professor Andrew Carr says the timing was coincidental.
He says it should not be assumed the US ban will encourage other countries to act similarly.
"Most countries decide their immigration policies based on a very narrow set of circumstances. Geography plays such a huge role, the environment and kind of countries around you, your own kind of national culture. So there's not a lot of overlap or flow of ideas or policy adoptions. In the long term, the US has encouraged countries to have more open and broader immigration systems, but I think we tend to overplay just how influential the United States has been."
Dr Carr says Israel's travel ban has more similarities to policies in China, where the government often blocks outspoken human-rights and Tibetan-rights activists from entering.
Sixteen Muslim-majority countries, mostly in the Middle East, also ban Israelis from entering their countries.
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