Under the new law, which annuls one issued in 2006, the spreading of any material that calls for "toppling, changing the regime or seizing power" is punishable by a prison sentence, Emarat Alyoum reported, citing the text.
The law gives the judicial authorities the same powers to punish "calls to disobey the principles of the political system" in the Gulf country, a federation of sheikhdoms.
Although oil-rich UAE has been spared the wave of uprisings that hit most Arab countries, the authorities have clamped down on Islamists and claimed in July to have dismantled a group plotting against state security.
Several of those arrested had been active on online social media networks.
Also under the new law, anyone convicted of "creating or running websites that deride or damage the reputation or stature of the country and its rulers will face a minimum jail sentence of three years," said The National, an English-Language daily.
This includes the president, the vice president, rulers and deputy rulers of the emirates and crown princes.
Anyone using electronic sites "to call for disobeying the laws and regulations of the state, as well as to call for demonstrations, marches and similar activities without obtaining a licence, also faces imprisonment," it added.
The United Arab Emirates has come under criticism over arrests.
A European Union resolution last month condemned "harassment," "restrictions on freedom of expression" and "illegal imprisonment" suffered by pro-democracy activists in the UAE, and demanded the "unconditional release of prisoners of conscience," which it says number 64.
The Gulf state dismissed the accusations as unfounded.