In an interview on Israel Radio Tuesday, Shalom said he intended to raise the issue at the next Cabinet meeting.
"The Islamic Movement's north branch leader, Sheik Raed Salah, and his deputy, Kamal Khatib, should be behind bars," Shalom told the radio station.
It is time for the state prosecutor's office to deal with the issue and act, he said. Failing to do so will be interpreted as a weakness by those who instigate violence, he said.
Shalom also accused the Palestinian Authority of attempting to assert control over East Jerusalem.
Other government ministers supported Shalom's plea. Interior Minister Eli Yishai said Jerusalem is the "sovereign, eternal and united capital of the Jewish state."
Salah told Haaretz Monday as long as Israel occupies Jerusalem and al-Aqsa mosque, the violence will continue. Israel must withdraw from these areas if calm is to be restored, he said.
The Islamic Movement was founded in Israel in 1971 and consists of two divisions, the extreme northern branch and the more moderate southern branch. Its aim is to advocate Islam among Israeli Arabs and operates on three fronts, one of which opposes the state of Israel and supports Palestinian nationalism.