Salah was accompanied by about 100 well-wishers, including Israeli Arab lawmakers, as he arrived at the prison in the city of Beersheba in southern Israel's Negev desert, an AFP journalist said.
At a farewell rally earlier in his home town of Umm al-Faham, in the north of the country, he exchanged hugs with supporters, local news agency Q-Press, considered close to the Islamic Movement, reported.
"It is an honour for me to enter prison to defend and protect Al-Aqsa and Jerusalem," it quoted him as saying.
Salah leads the radical northern wing of the Islamic Movement in Israel, which Israeli Prime Minister Benjamin Netanyahu ordered banned last year after accusing it of encouraging violent protest that contributed to the October outbreak of a wave of unrest that has so far killed 203 Palestinians and 28 Israelis.
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Most of the Palestinians killed were carrying out knife, gun or car-ramming attacks, Israeli authorities say.
Salah has previously spent time in Israeli prisons for offences ranging from incitement to spitting on a policeman to funding Palestinian Islamist militant group Hamas.
The convictions stem from a 2007 rally against Israeli construction work near the Al-Aqsa compound, in which he urged "all Muslims and Arabs (to) start an intifada (uprising) to support holy Jerusalem and the blessed Al-Aqsa mosque."
In clashes with Israeli police which followed, a number of officers were injured.
The protests reflected fears among Muslims that Israel was planning to change rules governing the site, the third holiest in Islam.
Revered by Jews as their most sacred shrine and known by them as the Temple Mount, the compound is a crucible of tensions in the Israeli-Palestinian conflict.