The plaintiffs, a man and a woman, had alleged that a law passed in 2013 against bestiality violated their "right to sexual self-determination".
"The complaint is unfounded," ruled the constitutional court.
The animal protection law forbids sex acts with animals or supplying animals to others for sex. Offenders face fines of up to €25,000.
In its ruling, the court said individuals must accept that government legislation is made in view of the overriding interest of the wider public.
That is the case here, as the protection of the welfare of animals from "unnatural sexual attacks" is a "legitimate aim", the court said.