The bill proposes that men and women inherit an equal share, violating the Koran, Sheikh Isyaka Rabiu said.
Gender activists have been pushing for the bill to end discrimination against women in a country with roughly the same number of Christians and Muslims.
Lawmakers say that public hearings will be held before the bill is passed, BBC reports.
Reverend Musa Asake, the secretary of the West African state's main Christian group, the Christian Association of Nigeria (CAN), told the BBC's Hausa service that he did not find anything wrong with the bill because in "Christianity inheritance is shared equally between male and female".
The senate has already rejected an earlier version of the bill, saying in March that it was incompatible with Nigerian culture and religious beliefs.
The BBC's Muhammad Kabir Muhammad in Abuja, says the new bill has been sponsored by a female senator, and is a watered-down version of the rejected Gender and Equal Opportunity Bill.
Nevertheless, it is still facing strong resistance from Muslim groups, including the influential Tijjaniya Brotherhood of which Sheikh Rabiu is a leader, our correspondent says.
The cleric continued, "whoever approves of it (the bill) is an unbeliever, not Muslim".
"I am appealing to all Muslim [senators] to never allow this bill to become law and if they do, we are going to tell all Nigerian Muslims not to accept it," he added.
Gender rights activists say the bill will help eliminate discrimination against women.
Muslim Senator Ubali Shitu said the bill still needed to go through various stages before it was voted on.
Lawmakers would only approve "those aspects that are beneficial and throw out those that we deem harmful", he added.
Human rights activist Bukky Shonibare had called the rejection of the bill in March a sad day for Nigerian women and said it showed "how backward we are".