The assault, which left four American diplomats dead in the Libyan city of Benghazi was triggered by a mob angered by a film deemed offensive to Islam that Afghanistan has condemned as "insulting".
In Yemen protesters also stormed the American embassy complex but were driven out by police, an AFP reporter said. In Egypt angry crowds pelted the US embassy in Cairo.
"He (Karzai) has cancelled his trip for the time being. He won't go, he's worried about possible riots over the release of the film," a presidential aide told AFP on condition of anonymity.
"He prefers to stay at home at such a critical time," the official added.
In Norway the foreign ministry confirmed that Karzai's arrival had been delayed because the president felt the need to be in Afghanistan after recent events.
Protests are expected to take place after weekly prayers in Afghanistan on Friday.
Karzai and US President Barack Obama discussed overnight how to "ensure that the circumstances that led to the violence in Libya and Egypt do not pose a threat to US forces or Afghans", the White House said.
Kabul said both men condemned the film and that Karzai expressed sympathy for the US deaths in Libya. It also said Karzai had a similar discussion with US Secretary of State Hillary Clinton.
The crudely produced low-budget movie, whose director goes by the name Sam Bacile and is believed to be Israeli American, pokes fun at the Prophet Muhammad, showing him sleeping with women and touching on themes of paedophilia and homosexuality.
The film has been promoted by controversial US pastor Terry Jones, who has drawn protests for burning the Koran and vehemently opposing the construction of a mosque near Ground Zero in New York.
Afghanistan is a devout Muslim country where anything seen as insulting to Islam is taken very seriously, often with a violent response.
Riots killed around 40 people earlier this year after US troops burnt copies of the Koran on a military base.
In an "emergency message" posted on its website, the US embassy in Kabul warned against possible protests in the coming days.
"We wish to remind US citizens that past demonstrations in Afghanistan have escalated into violent attacks on Western targets of opportunity. US citizens are therefore urged to avoid the areas of demonstrations if possible," it advised.
Around 117,000 NATO troops are based in Afghanistan helping Karzai's government put down a 10-year Taliban insurgency.