A statement by the federal department of foreign affairs (FDFA) in Bern said that authorities were in contact with the woman's family and "were making every effort to ensure the kidnap victim is released unharmed," but did not identify her.
Local reports said she was a Christian woman in her 40s named Beatrice who had lived in the ancient city for years and was active in the local community.
Officials at the Swiss government's Agency for Cooperation and Development office in Bamako and at the Swiss embassy in Dakar, which is also responsible for Mali, are in touch with local authorities, the FDFA said.
The government said it had advised its nationals to leave the country temporarily following the March 22nd coup and had been advising against travelling to Mali since December 2009 because of a higher risk of kidnappings.
"Because of the deteriorating security situation following the military coup and the advance of the rebels in the north of the country, since March 30th the FDFA has advised the Swiss nationals living in Mali to leave the country temporarily," it said.
Impoverished Mali was plunged into crisis when a group of low-ranking army officers launched a coup that toppled president Amadou Toumani Toure on March 22nd, saying the government had not done enough to stem a rebellion that Tuareg rebels rekindled in the north in January.
The Tuaregs and their Islamist allies took advantage of the power vaccum in the wake of the coup to sweep across the desert north of the vast country, seizing an area roughly the size of France in days.
The Ansar Dine Islamist movement, with the help of Al-Qaeda in the Islamic Maghreb (AQIM), then took control of Timbuktu on April 1st.
AQIM, which has bases in the north of Mali, operates in several countries in the region. It has abducted a number of Europeans in the past.