Police arrested the 43-year-old father, who also is German, in an apartment in downtown Adeje. He refused to say where the rest of his family was, Europa Press said. The man had reportedly moved to the island on a permanent basis. The woman and their two sons had arrived on Monday to visit.
More than 100 emergency workers and police, aided by helicopters, participated in the search. The bodies of the mother and 10-year-old were located Wednesday afternoon in a cave between two ravines at the base of the Teide volcano, which towers over Tenerife island, the Civil Guard said.
The bodies had signs of violence, Spain's El País newspaper reported, citing anonymous investigation sources. A local court that specializes in crimes against women has taken charge of the case and sealed the investigation.
The volcanic Tenerife island in the Atlantic Ocean is a popular holiday destination. Violence against women is a persistent problem in Spain, where more than 990 women have died at the hands of their partners or former partners since 2003, when official Spanish records on such slayings began.