The Swiss federal agency says FIFA handed over seized "IT data" to its officials.
The evidence gathering follows two weeks after FIFA's offices were raided for the investigation.
Switzerland's Attorney General Michael Lauber opened criminal proceedings "against persons unknown" two weeks ago in a case probing possible criminal mismanagement and money laundering in the World Cup bid contests won by Russia and Qatar.
FIFA filed the criminal complaint last November.
The Swiss agency says FIFA president Sepp Blatter and Secretary General Jerome Valcke are not suspects in the case.