The Swiss Catholic Lenten Fund and the Protestant agency Bread for all are calling on consumers to protest against the exploitation of workers and to ensure firms meet their social responsibilities.
The campaign follows an investigation of 27 suppliers in China, Thailand and the Philippines commissioned by the charities. The five brands in the firing line are Hewlett-Packard, Dell, Acer, Apple and Fujitsu Siemens.
"All forms of labour must respect human dignity," Charles RidorÃ© of the Swiss Catholic Lenten Fund told swissinfo.
"But in this sector - as in others - firms are relocating, leading to unemployment in our part of the world and exploitation in developing countries, with the clear aim of maximising profits."
RidorÃ© highlighted the low wages and the health risks faced by factory workers. The campaign group Students and Scholars Against Corporate Misbehaviour has labelled the electronics industry "one of the most toxic in the world".
Investigators say that during peak production workers put in 12 hours a day, seven days a week, plus mandatory overtime - all for SFr0.50 ($0.41) an hour.
The charities are calling for a ban on forced labour and child workers, non-discrimination and for staff to be allowed to form a union. They say they are willing to work with suppliers to help them improve conditions.
RidorÃ© said he hoped the initiative would achieve similar results to the fair-trade campaign targeting the textile industry.
The Swiss Catholic Lenten Fund and Bread for all are urging the public not to boycott the multinationals but to send in cards bearing the words, "High Tech - No Rights?"
"We are asking them to recognise their social responsibility along the entire production process and not just in Swiss salesrooms. If they have a code of conduct, they must make sure it is made known to all those participating in the production and assembly of their computers," explained RidorÃ©.
Responding to the campaign, Fujitsu Siemens Computers said social responsibility was a top priority.
"Fujitsu Siemens Computers has established a strict code of conduct for not only our own employees but also for our suppliers," said communications director Amy FlÃ©cher. "We demand the same standards of our suppliers worldwide, regardless of where they are based."
Hewlett-Packard Switzerland said it had "some of the most ambitious supplier standards in the industry" and was committed to its suppliers achieving them.
"If an external party identifies credible issues associated with a particular supplier, our policy is to investigate the situation and take appropriate corrective action," said Beat Welte, head of public affairs.
Apple said it too was committed to ensuring the highest standards of social responsibility, adding that it carried out regular audits of suppliers to ensure they provided safe working conditions and treated employees fairly.
swissinfo also contacted Dell and Acer but was unable to get a response ahead of publication.
swissinfo, FrÃ©dÃ©ric Burnand and Adam Beaumont in Geneva
The study was carried out by the Centre for Research on Multinational Corporations - a Dutch non-profit research and advisory bureau.
Investigators targeted suppliers for the five leading computer brands in Switzerland: Hewlett-Packard, Dell, Acer, Apple and Fujitsu Siemens.
According to the two Swiss charities behind the campaign, Hewlett Packard and Dell are the most proactive when it comes to labour rights.
* High Tech - No Rights? campaign (French) (http://www.campagneoecumenique.ch/spip.php?rubrique5)
* Swiss Catholic Lenten Fund (http://www.fastenopfer.ch/en/portal.asp)
* Bread for all (http://www.bfa-ppp.ch/eng/)
* Centre for Research on Multinational Corporations (http://www.somo.nl/index_eng.php)
* Students and Scholars Against Corporate Misbehaviour (http://www.sacom.hk/html/)
* Fujitsu Siemens (http://www.fujitsu-siemens.com/)
* Hewlett-Packard (http://www.hp.com/)
* Dell (http://www.dell.com/)
* Acer (http://global.acer.com/)
* Apple Switzerland (German, French) (http://www.apple.com/ch/)
- 116 Human Rights
- 204 Manufacturing