Police fanned out around the country on Monday ahead of the planned strike
Many Zimbabwean shops and businesses are open as usual despite opposition calls for a general strike to press for election results to be published.
Correspondents say many people cannot afford to lose a day's pay, while some say they have not heard of the strike.
Armed police and soldiers are on patrol, even though there are no plans for street protests.
The opposition says Morgan Tsvangirai defeated President Robert Mugabe and that the count is being rigged.
This is denied by the government, while the police accuse Mr Tsvangirai's Movement for Democratic Change (MDC) of "agitating for violence" by calling for the strike.
Meanwhile, South Africa's ruling ANC has said there is a crisis in Zimbabwe, directly contradicting President Thabo Mbeki.
The ANC said the "dire" situation could affect the whole region. At the weekend, Mr Mbeki said there was no crisis in Zimbabwe.
The MDC will be encouraged by the statement - it wants Zimbabwe's neighbours to put pressure on Mr Mugabe to accept the results.
Journalist Themba Nkosi in the second city Bulawayo told the BBC it was "business as usual", with public transport running as normal.
Zimbabwe is suffering from an acute economic crisis and just 20% of adults are believed to be formally employed.
MDC Secretary-General Tendai Biti on the need for a strike
Many others try to earn a living by selling vegetables or goods by the roadside.
The AFP news agency reported there were the usual long queues outsides banks and supermarkets.
"I did not even know about this stayaway," said Mthandazo Ncube, as he went to work in central Harare.
MDC Secretary General Tendai Biti said people should stay at home, adding that he feared any demonstrations would be ruthlessly put down.
"If you demonstrate in Zimbabwe, Mugabe will kill you. There is a de facto state of emergency at the moment," he told the BBC.
The police have banned any public demonstrations and warn that "those who breach the peace will be dealt with severely and firmly".
The MDC says that violence is increasing around the country, as Mr Mugabe's supporters prepare for a possible run-off.
Mr Biti told the BBC that two of its activists had been killed and 200 hospitalised after being assaulted by ruling party militias.
The MDC says its activists are being targeted in rural areas which voted for the opposition.
The election commission says it cannot release the results of the presidential election until a recount in some areas is completed at the weekend.
Shops may be open but they may not have much to sell
The MDC is challenging the recount in court. The recount of presidential and parliamentary results in 23 constituencies is to start on Saturday.
Zanu-PF wanted a recount in 22 constituencies, while an MDC recount request in one seat has also been granted.
The High Court on Monday dismissed an opposition petition to order the results to be released immediately, saying the reported anomalies should first be investigated.
MDC spokesman Nelson Chamisa told the BBC the High Court ruling in the capital, Harare, was "absolutely ridiculous and incredible".
Mr Mugabe's Zanu-PF welcomed Monday's ruling, denying the court was biased towards the ruling party.
Amid the ongoing tension, Mr Tsvangirai is currently basing himself in neighbouring Botswana.
His spokesman says this is to help him lobby regional leaders.
Independent tallies suggested Mr Tsvangirai won the poll, but took less than 50% of the vote, meaning he would have to face a run-off.
HAVE YOUR SAY
As much as I would want the man out, I will not participate in a strike as this is hopelessly ineffective against a regime of this kind
But the MDC says it would not take part in a run-off, saying a further election would mean increased violence - the first round was relatively peaceful.
The polls also saw Zanu-PF lose its parliamentary majority for the first time in Mr Mugabe's 28-year rule.
But it could be recovered if the ruling party is awarded just nine of the 23 seats subject to a recount.