Aceh introduced a version of sharia law in 2009 after it gained autonomy in a 2005 deal, ending a long-running separatist war. The Aceh laws regulate women's dress and public morality, require shops and other places to close at prayer time, and are enforced by a special unit. Punishments can include public caning.
On Monday, authorities in northern Aceh distributed a notice to government offices and villages informing residents of the proposed law, which would apply to adolescent girls and women. It states that women are not allowed to straddle motorbikes other than in an "emergency", and are not allowed to hold on to the driver.
Suaidi Yahya, mayor of the Aceh city of Lhokseumawe, said a ban was needed because the "curves of a woman's body" are more visible when straddling a motorbike than when sitting sideways with legs dangling.
"Muslim women are not allowed to show their curves, it's against Islamic teachings," he said, declining to give details of what the punishment would be for violators.
Last week, home ministry officials said they would try to block the law because it was discriminatory.
While rare in the west, riding side-saddle on a motorbike is common in much of south-east Asia, particularly for women wearing skirts.
Nurjanah Ismail, a lecturer on gender issues at the Ar Raniry Islamic Institute in Aceh's capital, Banda Aceh, criticised the proposed law.
"There is no need to question this practice, let alone regulate it, because people do it for safety," she said. "Women sitting in that way cannot be considered bad or in violation of sharia. Islam is beautiful, so do not make it difficult."
It is unclear how popular the sharia provisions are with locals in Aceh, which is devout by Indonesian standards but not to the extent of parts of Pakistan or the Middle East. Enforcement of the laws is patchy and mostly targets young men and women. Caning, when applied, is typically aimed at causing humiliation rather than pain.
Since 2005, many other regions in Indonesia have issued sharia-inspired bylaws that ban such things as alcohol or tight clothing, alarming rights activists and others who value the country's secular heritage.
President Susilo Bambang Yudhoyono's government, which relies on the support of Muslim political parties, has remained silent on the proposals.