"They were arrested yesterday. We suspect they were engaged in espionage and we are currently checking these accusations," said Kiril Rudenko, deputy spokesman for the self-proclaimed "People's Republic of Donetsk".
Rudenko could not confirm whether there were any foreigners among those held.
According to a local website, Novosti Donbassa, unknown gunmen burst into the Red Cross office in Donetsk and took seven people, including one French national, three local men and three from Kiev, France24 reported.
The website said they are currently being held in the regional administration headquarters in the city.