She was seized by unknown armed men from inside the ICRC compound at 20:00 local time (17:00 GMT) on Wednesday.
Police told Reuters they are searching for her. No-one has claimed responsibility for the abduction.
It comes a day after gunmen shot dead a Somali woman who worked for the World Health Organization, also in Mogadishu.
The unidentified attackers escaped and their motive remains unknown.
Decades of conflict have made Somalia one of the world's most dangerous countries for aid workers.
The targeting of foreign workers, however, has become far less frequent as security has improved in the Horn of Africa country in recent years.
"We are deeply concerned about the safety of our colleague," said Daniel O'Malley, the ICRC's deputy head of delegation for Somalia, in a statement.
"She is a nurse who was working every day to save lives and improve the health of some of Somalia's most vulnerable people."
Staff believe the kidnappers took their colleague out through a back door, avoiding security guards stationed at the main entrance of the ICRC compound, Reuters reported.
The Swiss-based agency, which has provided humanitarian aid in Somalia for years, would not provide further details except to say it was working with various authorities to secure their employee's release.
Somalia collapsed into anarchy in 1991 when war lords overthrew a military regime. Major armed conflict has since subsided, which allowed for parliamentary and presidential elections to take place in 2012.
However, al Qaeda-linked al-Shabab militants still regularly launch attacks in the capital and elsewhere in the country.