US authorities have refused to let five Cuban Grammy Awards nominees travel to Sunday's ceremony in Los Angeles.
Ibrahim Ferrer recently won a BBC Radio 3 world music award
Musicians up for best tropical Latin album award - including veteran star Ibrahim Ferrer - have not got visas.
Ferrer, 77, told press in the capital Havana: "I am not a terrorist. I couldn't be one. I am a musician."
A US diplomat in Havana said the US administration could suspend the entry of people deemed to be "detrimental to the interest of the United States".
The US has imposed economic and travel sanctions on Cuba for 40 years - and President Bush has strengthened the country's policy against Cuba and cut back on cultural exchanges.
Cuban vice-Culture Minister Abel Acosta accused the US of making a political decision to please Cuban-American voters in Florida.
"How can these musicians be considered terrorists?" asked Mr Acosta, who is also head of the Cuban Music Institute.
"Something as noble as music is being converted into a policy against Cuba."
Ferrer is the best-known of the nominees after appearing in 1999's Buena Vista Social Club film. He recently won BBC Radio 3's world music award for best artist from the Americas.
The other artists to be refused visas are Guillermo Rubalcaba, Amadito Valdes, Barbarito
Torres and the group Septeto Nacional Ignacio Pineiro.
But pianist Chucho Valdes, nominated for best Latin jazz album, has been granted a visa.
Similar rows blew up over visas for Cuban artists before the Grammys in 2002 and 2003.