The organizers of the demonstration - various left-wing campaign groups - have registered more than 15,000 participants, many of them Kurdish.
However, following calls for participation across Europe, police now believe at least 20,000 are planning to take part, including Turkish nationalists, Jacob said.
Turkey launched an offensive in northern Syria on October 9, saying it is targeting Islamic State extremists and Kurdish militias in the region.
Thousands of people took to the streets in cities across Germany last weekend to demonstrate against the offensive.
Experts have warned that tensions in Germany between people with Kurdish and Turkish roots could become much worse in light of Turkey's offensive in Syria.
On Tuesday, a protest by the Kurdish diaspora in Herne in north-western Germany over Turkey's incursion into northern Syria turned violent and left five people injured.
------------------------------------------------------------------------------------