Protests over the film, which depicts the Prophet as a womaniser and religious fake, have spread to several countries after Egyptian demonstrators scaled the US embassy walls in Cairo on Tuesday and tore down the American flag.
Sudan's Foreign Ministry also criticised Germany for allowing a protest last month by right-wing activists carrying a caricatures of the Prophet and for Chancellor Angela Merkel giving an award in 2010 to a Danish cartoonist who depicted the Prophet in 2005 triggering demonstrations across the Islamic world.
President Omar Hassan al-Bashir is under pressure from Islamists who feel the government has given up the religious values of his 1989 Islamist coup.
The official body of Islamic scholars called for the faithful to defend the Prophet peacefully, but at a meeting of Islamists, some leaders said they would march on the German and U.S. embassies and demanded the ambassadors be expelled.
"We have 5 000 mosques in Khartoum with 2 million people ... attending Friday prayers," said Salah el-Din Awad, general secretary of the scholars' body in Khartoum state.
"Tomorrow we will all got out to defend Prophet Mohammad ... We will do this peacefully but with strength," he told reporters after meeting government officials on Thursday.
The Foreign Ministry said in its statement: "The German chancellor unfortunately welcomed this offence to Islam in a clear violation of all meanings of religious co-existence and tolerance between religions."
US embassy officials said Islamists staged a small protest on Wednesday in front of the building, which is located outside Khartoum for security reasons.
US Secretary of State Hillary Clinton said Washington had nothing to do with the crudely made film posted on the Internet, which she called "disgusting and reprehensible".
Four US officials including the ambassador to Libya were killed in Benghazi on Tuesday after a protest over the film at the US consulate. Yemeni demonstrators stormed the US embassy compound in Sanaa on Thursday.
Egypt's Muslim Brotherhood, whose political party propelled the nation's president to power, have also called for a nationwide peaceful demonstration on Friday.
Sudan's Foreign Ministry did not mention the death of the US diplomat in Libya but urged Muslims not to attack anyone.
However, feelings were running high at the meeting of Islamists.
"Tomorrow we will go first to the German embassy and then to the American embassy," said Mohammed Ali Gezali, head of a group which says it wants to protect Prophet Mohammad.
"We demand the German and American ambassadors to be expelled," he said, while supporters shouted "Allahu Akbar" (God is Greatest).
Another speaker, Sheikh Nasser of the radical Hizb al-Tahrir al-Islami (Islamic Liberation Party), called on fellow Islamists to attack the two embassies - as well as the presidential palace for allowing the envoys to stay in the country.
Sudan used to host prominent militants in the 1990s, such Osama bin Laden, but the government has sought to distance itself from radicals to improve ties with the West.
Washington has tough trade sanctions against Sudan in place, with officials often criticising Khartoum for its human rights record.