The pair, both asylum seekers, were arrested on Sunday in Chiasso, near the Italian border.
“The man is the brother of the presumed perpetrator of the attack in Marseille,” a statement from Swiss federal police said, referring to Ahmed Hanachi, the 29-year-old who killed two women in the French coastal city on October 1st.
The man currently in Swiss custody is “known to foreign police services for his links to jihadist terrorist movements,” the statement added.
“His role in the Marseille attack, if he had one, is not yet clear.”
Federal police spokeswoman Cathy Maret separately told AFP that, in accordance with Swiss law, the detained husband and wife are due to be repatriated to Tunisia.
But that process will take several weeks at minimum and could be altered if another jurisdiction requests the couple's extradition.
Maret earlier said that police had information indicating the couple “could represent a threat to Switzerland's domestic security”
They were arrested at the migrant registration centre in Chiasso in Switzerland's Italian-speaking Ticino region, Maret added.
A French security source close to the investigation into the Marseille attack identified the man in Swiss custody as Anouar Hanachi.
The source said the arrests were requested by Tunisian authorities.
Swiss police would not confirm the identities of either the man or woman.
The news comes as one of Hanachi's other brothers, Anis, was arrested Saturday night in Italy, after French authorities issued an international arrest warrant.
Another one of his brothers and a sister were detained in Tunisia late last week and had been questioned by anti-terror investigators there. They have since been released.
Tunisian security sources have said they suspect both Ahmed and Anour Hanachi of being “extremists”.
Their father Noureddine has told AFP that he doubted his sons in Europe had been radicalized, adding that he had not heard from either for two months.
The Islamic State group has claimed responsibility for Hanachi's attack, but French investigators have not yet found evidence linking him to the jihadist organization.