He told Israel's Army Radio: "I assume that every sane person in the state of Israel, possibly the entire Jewish world, is shocked, because the significance is ... the destruction of the family unit in the state of Israel."
Gafni said he would consider presenting a bill to parliament that would bypass Tuesday's Supreme Court ruling and make recognition of all same-sex marriages illegal.
Moshe Negbi, a legal expert, said the court's decision was mostly symbolic because gay couples in Israel already had many of the rights of heterosexual partnerships.
Negbi said the significant changes were that they would now get the same tax breaks as a married couple and be able to adopt children.
Efforts by Israel's gay community to win approval for same-sex marriage face a major obstacle because Israel's religious authorities have a monopoly over Jewish marriage and divorce.
Yossi Ben-Ari, who petitioned the court along with his partner, Loren Shuman, brushed off Gafni's comments as a continuation of the ultra-Orthodox "frenzy" against Israel's gay and lesbian community.
Ben-Ari told Israel's Army Radio: "This is only the beginning of the battle. The courts here are very progressive ... but the battle is for the face of society.
"The battle for our rights doesn't end here, it is still very long."
Animosity towards gay people is one of the few issues that unites Jews, Muslims and Christians in Israel and the occupied territories.
Earlier this month, a planned gay parade in Jerusalem set off days of violence in the city's ultra-Orthodox neighbourhoods.