Mugabe appears undeterred by international pressure
The controversial media law was altered to take account of criticism from within President Robert Mugabe's Zanu-PF party.
Morgan Tsvangirai, leader of the opposition Movement for Democratic Change (MDC), told the BBC that the law was "the sign of a desperate regime trying to muzzle the press".
Condemnation also came swiftly from the United States and UK.
The UK Foreign Secretary, Jack Straw, said he found it "almost impossible to comprehend how free and fair elections can be held in Zimbabwe when such laws have been passed".
"I also condemn the press law," said US Secretary of State Colin Powell.
The European Union has threatened to impose sanctions if its observers are not allowed into the country by the weekend.
This threat now looks likely to come into force, the BBC's Hilary Andersson says.
But Mr Tsvangirai doubted that the presence of observers would make any difference to the outcome anyway.
"It's now up to the people of Zimbabwe to see what it can salvage from this situation," he said.
On Wednesday, Commonwealth foreign ministers called for an end to violence and intimidation in the country in the run-up to elections, but refused to back a UK call for Zimbabwe to be suspended from the body.
Concessions
Under the controversial proposals, foreign journalists would not be allowed to be based in Zimbabwe.
Reports deemed to cause alarm and despondency would be forbidden.
But in a concession to opponents of the bill, media organisations which are already registered in Zimbabwe would not have to apply for new licences as stated in previous drafts.
The new version also differs in allowing foreigners to take non-controlling stakes in Zimbabwean media organisations.
The government had originally wanted to pass the bill last year and debate has been delayed on several occasions following criticism from journalists, the international community and southern African leaders.
Journalists had earlier warned that they would ask the Supreme Court to declare it unconstitutional as soon as it is passed.
Election fever
The bill was passed as the contest for presidential elections in Zimbabwe officially began - with President Robert Mugabe and his main challenger, Morgan Tsvangirai, filing their nomination papers.
The poll in five week's time is expected to be the most fiercely fought since the country's independence in 1980.
Human rights groups are reporting a sharp increase in political violence in recent weeks.
The 77-year-old head of state is expected to hold his first two campaign rallies on Friday.
The Movement for Democratic Change leader said, when filing his papers at the court, that intimidation was still widespread across the country.
He said opposition officials were told they would be arrested if any slogans were chanted or party posters displayed at a rally scheduled on Sunday in Mutare in eastern Zimbabwe.
"This is not in the spirit of maintaining law and order and a spirit of free campaigning," he said.