But a tribal dignitary who is involved in negotiations to secure the hostages' release told AFP later that the kidnappers were demanding that the trial of fellow tribesman Abdelbaset al-Markashi be moved to their hometown Jaar from the main southern city of Aden.
However, "negotiations have failed," Abdullah al-Marakishi said.
For the moment the Red Cross workers appear to be alright.
"Our colleagues told us that they are fine," ICRC Middle East spokeswoman Dibeh Fakhr told AFP, confirming the three employees were being held by a group in southern Yemen since .
She withheld the names and nationalities of the captives, but local sources have told AFP a Swiss and Kenyan staffer as well as a Yemeni interpreter were seized by armed tribesmen in the city of Jaar, in Abyan province.
Kidnappers from Al-Marakisha tribe stopped the group's car and abducted the male Swiss staffer, witnesses said.
A tribal source said the Kenyan and the Yemeni interpreter insisted on staying with their colleague, even though the kidnappers told them they could go.
Their Yemeni driver fled.
The trio have been taken to a mountainous area north of Jaar, the tribal source said, requesting anonymity.
Fakhr said the motives for the kidnapping remain unknown, and the ICRC has not received any demands from the captors, while "negotiations are ongoing" to secure their release.
Last week, armed men from the same tribe briefly held two Indian ICRC employees in Jaar, before pro-government militia interceded for their release.
Gunmen from the same tribe are still holding two Egyptian technicians they seized from a cement factory in Abyan province on May 6th.
Hundreds of people have been abducted in Yemen over the past decade and a half, almost all of who have been freed unharmed.
Most kidnappings of foreigners are carried out by members of Yemen's powerful tribes who use them as bargaining chips in disputes with the central government.