Earlier, crowds stormed the German embassy, setting it partially on fire and raising an Islamist banner. The British embassy was also attacked.
One person was killed in Lebanon, while five were hurt in Cairo. There were also clashes in Yemen and Tunisia.
Protests began on Tuesday against the film, which was made in the US.
However, the film - clips of which were distributed on the internet - has no link to either Germany or the UK.
'Million-man march'
A spokesperson for the UK Foreign Office confirmed to the BBC that a demonstration was taking place outside the embassy in Khartoum, and said Sudanese police were at the scene.
However, the spokesperson could not say whether protesters had entered the embassy, or whether the demonstration was about the anti-Islam film.
The German foreign ministry confirmed all its staff in Khartoum were safe.
In Cairo, police firing tear gas pushed about 500 protesters back from the US embassy. The streets nearby have been blocked with barbed wire, concrete and police vehicles.
Islamist groups and others had called for a peaceful "million-man march" in the city, but a number withdrew those calls on Friday.
The Muslim Brotherhood of Egyptian President Mohammed Mursi said it would organise marches and sit-ins in front of mosques - but none outside the US embassy in Cairo.
After talks with Italian leaders in Rome, Mursi reiterated his government's determination to protect foreign diplomats on its soil. He also condemned the film as unacceptable.
In Lebanon, protesters in Tripoli, in the north of the country, set fire to a KFC branch, sparking clashes with security forces.
The protests began on Tuesday in Cairo. They spread to the Libyan city of Benghazi, where demonstrators stormed the US consulate, killing the ambassador and three other Americans.
