Afghanistan's Taleban rulers follow a purist form of Islam
The United Nations says it is concerned for the well-being of the group, who work for the international aid agency Shelter Now.
A senior Taleban official said those arrested, who include eight foreigners, had "confessed to the crime" and will be tried soon.
In January, the Taleban's supreme leader, Mullar Mohammad Omar, decreed that anyone convicted of trying to persuade an Afghan Muslim to convert would face the death penalty.
Material 'on computer'
The Taleban religious police say they caught two women - an American and an Australian - showing Christian material to an Afghan family on a computer in their home in the capital, Kabul.
The Taleban Deputy Minister for Promoting Virtue and Preventing Vice, Mohammad Salim Haqqani, told the French news agency AFP: "We have been following this group for a long time and finally on Friday afternoon we were able to capture the two women red-handed."
More arrests followed, including that of the group's German director.
The agency's offices and a school where the group was teaching 65 children were also closed down.
Mr Haqqani said the detainees are all being treated well and had no messages for their families or governments.
However, United Nations spokesman Letizia Rossana said the arrests were "a major concern" and followed an increasing trend of foreign aid workers in Afghanistan being harassed.
A spokesman for the American embassy in neighbouring Pakistan said officials had managed to contact Taleban officials, but were not been able to confirm if any Americans were among those arrested.
An embassy spokesman told AFP: "We are seeking a swift resolution to this issue."
Aid work
Shelter Now describes itself as a non-governmental organisation involved in food distribution, water supplies and helping street children.
The Taleban, however, says its activities are a front for propagating Christianity.
The Taleban militia, which controls 95% of the country, follows a purist form of Islam and takes a hard line towards minority religions in Afghanistan.
The regime provoked a storm of international criticism earlier this year for destroying two ancient Buddhist monuments, which it said were idolatrous, and for proposing members of Afghanistan's tiny Hindu community wear yellow stars for identification.