"We are deeply concerned about the safety of our colleague," said Daniel O'Malley, ICRC's deputy Somalia head.
"She is a nurse who was working every day to save lives and improve the health of some of Somalia's most vulnerable people."
The Red Cross said the attack happened around 8.00 pm local time (1700 GMT) when unidentified armed men entered its compound in Mogadishu, adding it is "in contact with various authorities to try and secure her release".
People working for the Red Cross in Somalia told AFP the gunmen appeared to have evaded the compound's security guards and snuck the nurse out through a back entrance into a waiting vehicle.
A government security officer said investigations were underway. "We have received information indicating a female western staff member was kidnapped from the ICRC office in Mogadishu," said Abdirahman Mohamed.
The abduction is the second attack on ICRC employees in Somalia in just over a week.
Abdulhafid Yusuf Ibrahim, a Somali national who had worked for the group for only five months, died on March 25 after an improvised bomb exploded beneath his car as he left the ICRC office.
Bombings, assassinations, abductions
Unlike many other international aid agencies working in Somalia, the ICRC does not base itself within the well-defended perimeter of Mogadishu's airport, which is protected by African Union soldiers.
The airport acts as the city's "Green Zone" housing foreign embassies and the United Nations which coordinates the humanitarian and political responses to Somalia's crises.
Germany's Foreign Minister Heiko Maas, who is visiting Ethiopia and Tanzania this week, told journalists in Addis Ababa he would not comment "on any hostage cases".
"I have deep respect for all people, especially people from Germany, working abroad in order to help others," Maas added.
Somalia, which collapsed into civil war in 1991 and has been the site of an Al-Qaeda-linked Islamist insurgency since 2006, is one of the most dangerous countries for aid workers, but abductions remain relatively unusual.
In the past, foreigners, including journalists and aid workers, have been kidnapped by armed gangs or Shabaab militants and held for ransom, sometimes for years at a time.
Terrorist bombings and assassinations are common and frequently claimed by the Shabaab which is fighting to overthrow the internationally backed government in Mogadishu.
International aid agencies, including the independent Switzerland-based ICRC, provide health care and other basic services in the war-torn country and are regarded as supporters of the government by the Shabaab and as a ready source of income by other militants and armed gangs.
On Tuesday a local employee of the World Health Organization (WHO) was shot in Mogadishu.
The WHO said in a statement Wednesday it was "shocked and saddened" by the killing of Mariam Abdullahi Mohamed, "a dedicated frontline worker".
Between 2008-12 piracy off the coast of Somalia became a big business with crew members and their ships held for million-dollar ransoms, but in recent years attacks have become rare.
Gradually improving stability in Somalia allowed the holding of limited elections in 2016, but insecurity remains widespread.
In October, Somalia suffered its deadliest-ever bombing, with over 500 people killed in an attack blamed on the Shabaab.
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