Their hit, La Bicicleta, won last year's Grammy Latino.
Cuban musician Livan Rafael Castellanos claims that Shakira and Vives copied a line and part of the chorus of his 1997 song Yo Te Quiero Tanto.
The complaint was filed at a court in Spain, where Shakira lives.
A spokesman for the court said the case centred around an intellectual property problem and focuses mainly on the melody and the lyrics of the choruses of both songs.