"The families decided to cancel a public funeral which was planned for Friday morning," said Shia cleric Sayid Jasim Muhammad.
"This decision was taken after a mortar shell burst at 8.45am (0545 GMT) at the site of the attack," he said, adding the families did not want to risk another calamity.
Forty-seven Iraqis were killed and more than 80 wounded in the bombing on Thursday as mourners gathered next to the Sadrin mosque, where a service was being conducted for Hisham al-Araji, the Mosul representative for Muqtada al-Sadr.
Muhammad recalled the moment when the explosion ripped through a funeral tent at 5.20pm (1420 GMT) as food was being served to mourners.
"A ball of fire shot out, followed by falling debris, and panic swept the outdoor tent next to the Sadrin mosque," he said.
"No one among the survivors had the time to see the bomber. The others who caught a glimpse of him are dead," he said.
The bloodshed came as Shia and Kurdish politicians in Baghdad said they had overcome a major stumbling block to forming a new coalition government.
Shia mosques and funerals have become frequent targets of attacks. Last month, bombers attacked a number of them during the Shia commemoration of Ashura, killing nearly 100 people.
Mosul has been a focus for fighting, and the scene of many bombings, drive-by shootings and assassinations targeting the country's security services, majority Shia and people thought to be working with US-led forces.
Family members and politicians agreed there would be no joint funeral in Mosul on Saturday because of the "fear of another attack like this one," said Hamid Zain al-Ali, a member of the Al-Sadr Movement, whose fighters rose up against US troops several times in 2004.
Instead, families will hold private funerals across the city, and the Al-Sadr Movement will provide armed guards for each of the tents that would be used.
A similar decision was taken on 1 March in Hilla, south of Baghdad, when fears that crowds of Shia mourners would be targeted forced the authorities to cancel an elaborate funeral procession for some of the 125 people killed in a bombing there.