Former Interior Minister Gideon Saar stands to the right of Netanyahu and has argued for a tougher line against the Palestinians.
The party's approximately 116,000 eligible voters had until 22, Swedish time, to decide who should continue to lead the party. The votes are expected to be completed first on Friday morning.
Political analysts expect Netanyahu to win the battle, but a relatively even result would weaken his position within the party he has led for 20 years.
Netanyahu has been Israel's prime minister since 2009. Last month, he was indicted in three separate corruption cases, but he denies the charges being brought against him for fraud, bribery and infidelity.