Spokesmen for the three Muslim organisations said they were preparing an official request for an investigation to be launched into how the books found their way on to the exhibition's shelves.
Muslim organisations and activists described the books as "hypocritical" and aimed at staining the reputation of the prophet, his family and companions.
The organisations also called for the closure of the three Iranian Cultural Centres in Sudan
, which they accuse of promoting Shia beliefs in the country
The Islamic Fiqh Board, an organisation linked to the Sudanese presidency, has issued a statement saying the books have been confiscated because they contained thoughts contradictory to Islam's basic beliefs.
Dr Abd al-Hay Yusouf, a member of the Islamic Fiqh Board, told Al Jazeera that the books were brought into the country through the diplomatic mail of the Iranian embassy.
He said: "We sensed the real activities of the Iranian cultural centres in Sudan a long time ago, and we warned the government that the centres are dedicated to spread Shia in Sudan, but, unfortunately, they did not listen to us.
"There are three Iranian Cultural Centres in Sudan, their Iranian employees move about the country freely, while the Sudanese embassy employees in Iran are not allowed to contact anybody in Iran unless through the Iranian foreign ministry."
Ibrahim al-Ansari, the Iranian cultural attache in Sudan, dismissed the allegations of Shia missionary groups, stressing that the Iranian Cultural Centres are open for all Muslim sects.
He said: "Our work based on a saying from the Islamic literature 'Believers are brothers'. We are not sectarians and I am a Shia, but I do pray in Sunni mosques. We respect and admire people's beliefs even if they do not agree with ours."
The Supreme Council for Co-ordination among Islamic Groups has warned of a widespread Shia missionary operation in Sudan, and said at the press conference in Khartoum on Tuesday that several Sudanese villages have converted to the Shia sect.
Yusouf said: "I think it is an exaggeration to say many villages. There is only one village called Um Dam in Kordfan converted to Shia. However, this does mean that we should not underestimate the activities of Shia missionaries in the country."
The Persian version of Shia doctrine is based on the belief that Ali, a cousin of Prophet Muhammad and his son-in-law, should have been the first caliph or successor after the prophet's death, and hold Aisha, the prophet's wife and the prophet's companions responsible for depriving Ali of that "right".
Sunni Muslims reject the idea and insist that Prophet Muhammad's companions were much more honourable than to plot against the prophet's cousin, and hold those who disparage the prophet's companions as "criminal".
Iran maintains cultural centres worldwide, which report directly to the Iranian cultural attaches.