The court is expected to deliver its ruling in the coming months.
The 2011 law does not make a boycott call a criminal offence, but rather a civil issue that could trigger lawsuits demanding compensation. There is no precedent of this happening yet.
The collection of rights groups yesterday said the law infringes on the right to free speech while defenders of the law say it prohibits discrimination based on geography.
The appeal comes against a backdrop of an international boycott campaign against Israel's settlement policies in captured territories claimed by the Palestinians. Israel officials have derided the campaign as anti-Semitic since it holds Israel to a double standard.
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Haggai El-Ad, head of the Association of Civil Rights in Israel, said that a boycott is a legitimate form of protest and that the Israeli law was politically motivated since it only applied to those targeting the settlements.
Deputy Foreign Minister Zeev Elkin, who initiated the bill, said the aim was to prevent discrimination against people based on where they lived. He said Israel has to defend itself against those aiming to harm it.
More than 550,000 Israelis live in the West Bank and east Jerusalem, contiguous areas captured in the 1967 war, among roughly 2.5 million Palestinians.
Some Israelis see a big security risk in giving up the West Bank, which commands the highland over central Israel. Many religious Jews see it as their biblical heartland.