Kuwaiti authorities are especially wary of political gatherings that could stir tensions in the Gulf Arab state, where expatriates make up around two-thirds of the 3.8 million population.
Foreigners are not allowed to hold political events and there are restrictions on public rallies held by Kuwaitis.
The source, who declined to be named, did not give further details.
Kuwaiti newspaper al-Watan said on Sunday that the 15 were traveling by bus south of the capital on Saturday. They were seen beating drums and waving, the report said, and planned to join other Egyptians to express their support for Sisi before they were arrested by police.