Last month, the court found Rubiales guilty of sexual assault and fined him over 10,000 euros in a case that sparked a nationwide furore.
The ruling also acquitted him and three co-defendants of a charge of coercion. The prosecution had sought 2-1/2 years' prison for the former soccer federation chief.
In the appeal seen by Reuters, prosecutor Marta Durantez requested the trial be repeated, arguing that evidence and many of her questions were not admitted.
Durantez said that the fine and the additional 3,000 euros in compensation awarded to Hermoso were very low.
Rubiales and Hermoso have said they will appeal the ruling.
The kiss at the 2023 World Cup awards ceremony in Sydney provoked a heated debate in Spain about sexism in women's football and wider Spanish society, prompting a movement similar to the 'Me Too' campaign on social media.
The ensuing scandal overshadowed Spain's victory in the tournament.