All forms of electronic media like Internet-based news services, bulletins, publications, newspaper and television station portals and commercial services are subject to the new law.
Thirty-seven members including cabinet ministers voted for the law and four MPs opposed it.
Those who voted against the legislation said it would further curtail freedom of speech and expression.
"I believe that the government wants to use this law like the others to curb freedoms," said MP Jamal al-Omar, who added that the legislation breaches the Gulf state's constitution.
Information Minister Sheikh Salman Humoud al-Sabah said the law only regulates the web media and does not apply to personal accounts like blogs.
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Under the law, all web-based publications require a government licence and their violations will be referred to the country's media law which stipulates jail terms for several offences.
Amnesty International on Tuesday denounced a "repressive" cybercrimes law in Kuwait, warning that it would further muzzle free speech.
The law, which took effect on Tuesday, criminalises online expression including criticism of the government, religious figureheads or foreign leaders.
Dozens of people in Kuwait have already been arrested and prosecuted -- some jailed -- under other legislation for comments made on social media sites such as Twitter.
The cybercrimes law, passed by parliament in June, stipulates 10-year jail terms and fines of up to $165,000 for online crimes, especially those related to terrorism.
Creating a website for a "terrorist" group or publishing news about the group on the Internet to try to raise funds carry a punishment of 10 years in jail.
Activists have criticised the government for issuing many legislation to impose tighter controls on the media.