Republican People's Party (CHP), the main opposition party, has denounced Imamoglu's detention as politically motivated.
The CHP has called on its supporters to protest peacefully and lawfully in response to the incident.
University students marched with the slogan: "We are not scared, we won't be silenced, we will not obey."
Last year, CHP surprised the world by winning all of the largest Turkish cities, including Istanbul and Ankara, in municipal elections.