A new law in Belarus will restrict access to foreign websites and force internet clubs and cafes to report users visiting sites registered abroad.
The law, which takes effect on Friday, says anyone selling goods or services to Belarus citizens on the web must use the .by Belarusian domain name.
That would make it illegal for firms like Amazon or eBay to sell goods to customers in Belarus.
Fines for breaking the law range as high as 1m Belarus rubles (£77; $120).
The law says people offering internet services to the public - whether at a cafe, club or in their own home - will face fines if their customers visit foreign websites and such visits are not properly recorded and reported.
Anyone found accessing "extremist" or "pornographic" websites will also be fined, the law says.
President Alexander Lukashenko has been in power in the ex-Soviet republic since 1994.
His muzzling of the opposition has been condemned by the EU and US, who have imposed travel bans and asset freezes on him and dozens of his associates.
At the end of December the Belarus opposition website Charter 97, run from outside Belarus, was disabled by a cyber attack.
The site's chief editor Natalya Radzina told the US-based Committee to Protect Journalists that the attackers had deleted archives and posted a false news story about opposition presidential candidate Andrei Sannikov.
Last May Mr Sannikov, co-founder of Charter 97, was jailed for five years for organising mass protests during the December 2010 presidential election.
Ms Radzina, who works in exile in neighbouring Lithuania, said the hackers got into the website by using a password, probably by sending malware to an editor's computer.
In December 2010 the authorities cracked down on protests against alleged vote-rigging in the presidential election.
More than 600 people were detained, including seven of the election candidates.
International monitors said the contest, in which Mr Lukashenko officially won 80% of the vote, was deeply flawed.
The UK's Europe Minister David Lidington says the UK is pursuing "all means possible to keep up the pressure for the release and rehabilitation of prisoners and for the promotion of democracy, human rights and the rule of law in Belarus".
Lawyers in Belarus say it is too early to tell what impact the new law will have, according to Euroradio.fm, an independent Belarusian news and music website.
A Belarusian advertising agency, RG Media, which does business with foreign websites, also said the new law "does not look very clear". "We have no idea how it will affect us," the company told Euroradio.
The Belarus interior ministry told Euroradio that any policeman would have the power to enforce the new law.