Cuban culture minister Abel Acosta said the delegation had planned to travel on Friday, but were still awaiting visas on Tuesday - effectively preventing their attendance at the Los Angeles ceremony.
The musicians affected include jazz pianist Chucho Valdes, members of the group Sintesis, guitarist Rey Guerra and rapper X Alfonso.
Mr Acosta said that visa restrictions were aimed at "limiting the cultural exchange" between Americans and Cubans.
Officials at the US Interests Section in Havana, Cuba have not commented on the issue.
Tipped
Last year the awards ceremony, originally scheduled for 11 September, was postponed and replaced by a low-key affair in Miami.
This year Colombian singer Carlos Vives is tipped to take home six Latin Grammys - including album, record and song of the year.
Other multiple nominees include salsa great Celia Cruz, Colombian rocker Juanes and Spanish pop star Alejandro Sanz.
The ceremony, at Hollywood's Kodak Theatre, will be hosted by singer Gloria Estefan and actor Jimmy Smits.
The Latin Grammys cover some 40 different categories of music, including lesser-known styles like flamenco, ranchero and norteño.
"It's important not only for the Latin music industry but also for the audience to see that there are so many talented artists out there," said Bruno Del Granado, president of the record label Maverick Musica.
But the Latin Grammys ceremony will also include the mainstream pop acts Justin Timberlake, Backstreet Boy Nick Carter and actress-singer Jennifer Love Hewitt.
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