The central bank's sharia board was meeting on Sunday to finalize the law, said Muhammed Qaseem Rahimi, director general of the central bank's Financial Supervision Department. It will then go to the Justice Ministry and parliament for approval.
"Most of the people who can access banking services don't use them just because of the interest, which is not allowed in Islam," Rahimi said.
"The demand for Islamic bank services is very high in banked and unbanked populations of Afghanistan."
Of 17 banks in Afghanistan, six have Islamic banking windows. The central bank hopes to approve the creation of fully fledged Islamic banks after the law is passed, Rahimi added.
Total deposits stood at $3.58 billion as of August 2010, according to a central bank report. But bankers estimate that there is close to $30 billion in circulation that remains untapped by the banking sector.
An Islamic banking law could revive an industry hit by scandal in recent months.
The central bank took over Kabulbank in September, the country's largest private bank, after irregularities of about $579 million raised red flags with authorities.
The crisis added another layer of uncertainty for the country, which already struggles with record levels of military and civilian casualties as well as corruption concerns.
But Islamic banking could renew trust in the sector, said Alam Hamdard, Kabulbank's head of Islamic banking.
"The crisis showed Islamic banking provides more transparency," he said.
"We could show them that their money was safe and secure in tangible projects that were being developed."
Hamdard said Islamic bank customers at Kabulbank did not withdraw funds at the same level as conventional banking customers during the scandal.
But reaching the conservative masses and educating them in how Islamic banking differs from the conventional system is a challenge, with some bankers taking to the airwaves or sitting down at religious gatherings in rural areas to preach Islamic finance.
"Our ultimate goal is to shake out all the money that is lying in pillows and not with the economy in order to contribute to the rebuilding of Afghanistan," Khan Afzal Hadawal, chief executive officer of Bank-e-Millie Afghan, said by telephone.
Hadawal said Bank-e-Millie's Islamic banking business has $15 million in deposits and that is projected to rise to $50 million by the end of the year as demand grows.
The Islamic banking sector in Afghanistan could attract up to $6 billion in five years, he said, if the sector starts to offer products such as Islamic credit cards, debit cards and automated teller machine facilities.
