The law, which was passed in March, comes as Prime Minister Benjamin Netanyahu fights corruption charges that relate to previous stints in office.
The measure has provoked fury in Israel, with opponents accusing Mr Netanyahu of drafting a law that is tailor made to relieve him of his legal battles.
Evading prosecution for these charges is viewed by critics as a key reason behind Mr Netanyahu’s wider push to drastically reduce the power of Israel’s judiciary, a cause that is championed by his right-wing coalition.
The planned overhaul includes changes to the way judges are selected, the removal of the Supreme Court's ability to strike down laws on the basis of them being unreasonable, and amendments to the way in which the government can receive legal counsel.
Critics say the plans would eradicate checks and balances, effectively ending democracy in Israel.
Supporters say they are needed to curtail an overly zealous judiciary that has too much power to quash laws proposed by democratically elected governments.
Passage of the law being deliberated on by the High Court on Thursday would mean only the government and parliament could declare a prime minister incapacitated, and only on medical grounds. Seventy-five per cent of cabinet ministers and 80 per cent of parliamentarians would need to approve.
The court is unlikely to annul the legislation, but it could take measures to delay its passage until after Mr Netanyahu leaves office.
The charges levelled against Mr Netanyahu relate to breach of trust, bribery and fraud.
Investigations into Mr Netanyahu began in 2016. He has denied the charges throughout.
The verdict on Thursday’s hearing will be published in mid-January.