"Our forces have started deploying in Jerusalem and the town of Bnei Brak [near Tel Aviv] where two major demonstrations organised by Orthodox Jews are due to take place," Micky Rosenfeld, a police spokesman, told the AFP news agency.
"These demonstrations have been authorised and are due at 1:30pm local time (10:30 GMT) and around 4:30pm respectively."
Dudi Cohen of the Israeli police has put his forces on a high state of alert, only one step below the maximum level, the Israeli public radio report said.
Parents who defy the ruling are to be imprisoned on Thursday for two weeks for contempt of court.
Israel's supreme court had given them until Thursday to send their children back to school or face jail, in a case involving around 40 Slonim Hassidic couples, whose roots are in eastern and central Europe.
The parents, who live in the settlement of Immanuel in the occupied West Bank, are refusing to let their daughters study at the Beit Yaakov girls' school alongside girls of Sephardi origin, originating from North Africa or Asia.
One Israeli newspaper likened the case to America's use of troops to enforce desegregation in the 1950s.
Late on Wednesday, officers used water cannon to disperse around 200 Orthodox Jews who protested in Jerusalem by throwing stones at police and disrupting traffic, Rosenfeld said.
No one was injured in the protest late Wednesday, and police made no arrests, Rosenfeld said. Talks were under way with a view to reaching a last-minute compromise ahead of Thursday's protests.
Benjamin Netanyahu, the Israeli prime minister, appealed for calm in a statement issued on Wednesday.
"At this critical moment, when Israel faces existential threats from our enemies, I call on all sides in the matter to show restraint, respect the law and solve the problem peacefully and amicably," the Haaretz daily reported.
Shimon Peres, the Israeli president, was due to hold talks with senior figures in the rabbinate to try to defuse the situation, Israeli public radio said.