"Last night we lit the fifth Hanukkah candle with all the family present before we were sadly obliged to send Kaiya to quarantine as required by law," Netanyahu wrote Friday in a Facebook post reported by media Saturday.
The premier said the experience brought home to him "flaws incompatible with logic and compassion" in Israel's public health regulations, which mandate that dogs who bite, even if they have received all the necessary inoculations, be confined for 10 days.
The mixed-breed bitch was adopted by the Netanyahus from an animal shelter in July.
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Kaiya nipped lawmaker Sharren Haskel from the prime minister's Likud party as well as the husband of Deputy Foreign Minister Tzipi Hotovely during a festive candle-lighting ceremony on Wednesday night.
Neither was badly hurt during the event at the premier's official Jerusalem residence.
Netanyahu tweeted a photo of himself and his new dog in August.
"How much light Kaiya brought into our home!" he wrote of the 10-year-old. "If you want a canine, find an adult dog to rescue. You won't regret it!"