But the "You Stink" campaign said the decision did not mean it was giving up.
The move comes after two days of demonstrations in the capital descended into clashes in which dozens of protesters and police were hurt.
Prime Minister Tammam Salam has appealed for calm and threatened to resign over the crisis.
In a televised address on Sunday, he warned that Lebanon was heading towards collapse, with the country's "political garbage" crippling his unity cabinet.
Thousands of people gathered outside the prime minister's office in central Beirut on Sunday to protest against the government's failure to have the large piles of rubbish which have been building up in the capital for weeks removed.
Chanting "the people want the downfall of the regime", some protesters threw rocks and sticks at riot police and lit fires. Officers responded by firing water cannon and tear gas.
The clashes left at least 44 demonstrators and 30 police officers injured, officials said. Dozens of people were also injured on Saturday, when police fired rubber bullets.
Like the issue of electricity in Iraq, the failure of a public utility in Lebanon - rubbish collection - has brought to a head simmering, chronic public indignation over a deadlocked political system riddled with corruption, inefficiency and sectarianism.
As the embattled Prime Minister Tammam Salam pointed out, it is this issue that threw the spotlight on the "political rubbish" that is the real problem - one that has paralysed his own cabinet and the twice-prorogued parliament from taking effective decisions on any issue.
Behind the political stagnation is the unbending stand-off between the two major political blocs, divided primarily over attitudes to the Syrian regime - the Iranian-backed Hezbollah and its mainly Shia allies on one side, and the Saudi-backed, mainly Sunni pro-Western 14 March movement.
Mr Salam's warning of an imminent collapse should be a wake-up call to those blocs that it is time to collaborate on solutions, not least to the 15-month vacancy at the country's presidency. That seems unlikely, with regional struggles as unresolved as they are.
Protesters are also broadening their demands to include an end to the pervasive sectarian political system, something that is even harder to imagine.
But public pressure is mounting. If it can at least get the rubbish collected and safely disposed of, that will be a start.
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On Monday, the campaign announced that the demonstration planned for Monday evening had been postponed.
"The movement has not and will not stop," a statement on its Facebook page said. "Postponing from today to another date this week is not a retreat. We need to reassess and organise our demands."
You Stink leader Hassan Shams earlier blamed "infiltrators" for the violence over the weekend. "We started peacefully, and we will continue peacefully," he told New TV.
The protests have been largely co-ordinated by You Stink, which was formed when rubbish began piling up on the streets of Beirut and neighbouring areas after the country's largest landfill was closed last month, with no ready alternative.
Activists blame political paralysis and corruption for the failure to resolve the crisis.
Fouad al-Hassan, a 65-year-old actor, told the New York Times that he had decided to attend Sunday's rally because he wanted to "change the system".
"We want new blood or the country will stay the same," he added.
Lebanon has been without a president for more than a year, while members of parliament have extended their own terms until 2017 after failing to agree on a law to govern fresh elections.
The conflict in neighbouring Syria has also exacerbated political and sectarian divisions, and resulted in the arrival of 1.1 million refugees, putting a strain on the economy and public services.
Mr Salam said that if a cabinet meeting scheduled for Thursday was not productive on several issues, including the rubbish crisis, "there would be no necessity for the government after it".
"I warn that we are going towards collapse if matters continue," he added.
"Frankly, I have not and will not be a partner in this collapse. Let all officials and political forces bear their responsibilities."
The prime minister also warned that the government, which brings together all the main Lebanese parties, would be unable to pay civil servants' salaries next month and risked being classified a "failing state".
If Mr Salam were to resign it could trigger a constitutional crisis because his replacement has to be appointed by the president.
Organisers of protests over the failure of Lebanon's government to clear rubbish from the streets of Beirut have postponed a rally planned for Monday.