Micky Rosenfeld, an Israeli police spokesman, said Salah would be investigated "on suspicion of incitement of violence ... and racism".
Salah told the Reuters news agency this week that he had called "on the Islamic and Arab world for an intifada to support al-Aqsa".
Israel's Haaretz newspaper also quoted Salah as saying: "[Israel] wants to build their temple while our blood is on their clothing, on their doorposts, in their food and in their water."
Threat to foundations
A Jerusalem court earlier this month banned Salah from coming within 150m of the Old City walls for two months, after finding him guilty of participating in a banned demonstration against the work.
Israel announced last week it would freeze plans to build the new walkway and accepted an offer by a Turkish team to inspect the dig.
Muslims say that Israel's work could damage the foundations of parts of the Al-Aqsa compound.
Israel captured the Old City and the rest of Arab east Jerusalem in the 1967 Middle East war and annexed the area as its capital in a move not recognised internationally.
Palestinians want east Jerusalem to be the capital of a state they hope to establish in the West Bank and Gaza Strip.