The IPO from Sunday, making NCB the last Saudi bank to go public, is expected to be one of the largest in the world this year.
"It will be very, very highly watched", said Beshr Bakheet of the privately-held Osool and Bakheet Investment Company.
Abdullah al-Mutlaq, a member of the kingdom's official Council of Senior Ulemas, said on television that the IPO is haram, or forbidden under Islamic tenets which ban usury.
"What is clear to me now is that it is not permissible," he said, adding that many of the bank's investments were already haram.
Will investors buy or will they back off because of what some religious authorities are saying, he asked.
Only three of Saudi Arabia's 12 banks are fully compliant with Islamic sharia laws, while the others offer sharia-compliant products along with conventional banking services.
NCB's sharia advisory council on Thursday declared the share offer to be acceptable under Islamic law.
"After much thought and deliberations regarding the issue, the bank considers the IPO in the bank's stock to be permissible according to sharia," it said in a statement obtained by AFP.
Saudi Arabia is OPEC's biggest oil exporter and its economy has been one of the best performing in the Group of 20 leading nations, according to the International Monetary Fund.
An NCB prospectus says the bank will offer 300 million shares to the public at 45 riyals (USD 12) each, potentially valuing the IPO at USD 3.6 billion.
Another 200 million shares will be allocated to the state pension agency.
The ultra-conservative Wahhabi Islamic tradition applies to both religious and political life in the oil-rich Gulf kingdom.
