The reports - which had yet to be confirmed by police spokesman Mickey Rosenfeld - said Salah had been detained on the roof of an East Jerusalem building.
The reports said the arrest had been decided after consultations between police and the prosecutor’s office.
Israeli ministers earlier Tuesday had called for the Islamic Movement to be outlawed, accusing it of incitement after days of unrest in Jerusalem.
The leaders of the Islamic Movement, an organization which is strong in Arab towns and villages in northern Israel, “must be behind bars,” Israeli Vice Prime Minister Silvan Shalom said.
“They are operating a system of incitement of the masses, raising funds ad dragging everyone behind them, including also Arab lawmakers, whose automatic support for Arab rioters one is (we are) fed up with,” charged Shalom, of the ruling Likud party and a relative hawk.
The Old City of Jerusalem remained highly tense Tuesday, after days of street clashes, and verbal warfare between Jewish and Muslim leaders, centering around a flashpoint holy site - the Temple Mount/Holy Sanctuary.
The compound houses the al-Aqsa mosque and is the third holiest site in Islam, marking according to tradition the spot from where the Prophet Mohammed ascended to heaven.
But it also contains the ruins of the Jewish biblical temple and as such is the most sacred site in Judaism.
The latest tensions erupted Sunday last week, when according to Israel a group of Christian tourists made a pre-arranged organized tour of the compound under Israeli police escort.
Rumours soon spread that they were Israeli settlers seeking to symbolically re-inaugurate the ruined Biblical temple at the site, on the eve of the Jewish Day of Atonment.
Israeli leaders accused Sheikh Salah of incitement by calling on supporters of his movement to help “defend” the Aqsa mosque based on a senseless rumour.
Since then, Muslim youths have clashed with Israeli police, throwing stones and bottles. Police have restricted access to the mosque to men with Israeli identity cards aged 50 or older to avoid an escalation in the unrest.
On Monday afternoon, an Israeli military police officer was stabbed in the neck and moderately injured by a Palestinian teen from East Jerusalem, as he boarded a bus at a military roadblock on the city’s outskirts for a routine check.
Police further beefed up security in the city, as thousands of Jewish hikers were participating in the traditional Jerusalem March, an annual pilgrimage event that is part of celebrations for the week- long Jewish holiday of Tabernacles or Sukkot, which began Friday.
Police were also on high alert ahead of the Muslim Friday prayers at the Aqsa mosque.
Sheikh Yusuf al-Qaradawi, the head of the international association of Muslim scholars, at a news conference in Cairo Monday called on Arabs and Muslims observe a “day of rage” in support of the Aqsa mosque this Friday, against the “Zionist dangers” threatening it.
Shalom accused also the Palestinian leadership of being behind the incitement revolving around the mosque. Other ministers and lawmakers made similar remarks.
“The Palestinian Authority is trying to place East Jerusalem into its realm of responsibility, into its realm of jurisdiction. And it is using the masses to do so,” he told Israel Radio.
Chief Palestinian negotiator Saeb Erekat countered by accusing Israel of “deliberately escalating” tensions, “to further entrench its occupation of East Jerusalem” and to “scuttle diplomatic efforts aimed at peace.”
“Israel is lighting matches in the hope of sparking a fire,” he said in a statement sent to journalists Tuesday.
Sheikh Salah himself told the Arabic al-Jazeera network Tuesday that the calls for outlawing his movement were “not new” and that if faced with the choice, he was willing to sit in jail for the “right to defend” the Aqsa mosque.
The Islamic Movement has a strong presence in municipalities of Arab towns and villages in northern Israel. It is not represented in the Israeli parliament, however, because it boycotts national elections as it does not recognize Israel.