It was discovered on 9 October 1989, by Japanese astronomer Yoshiaki Oshima at the Gekko Observatory east of Shizuoka, Japan.

[12] On 14 May 2021, the object was named by the Working Group for Small Bodies Nomenclature (WGSBN), after Medesicaste from Greek mythology, who was an illegitimate daughter of King Priam and wife of Imbrius.

[3] Before Medesicaste was named, it belonged to a small group of only 8 unnamed minor planets with a designated number smaller than 5000.

A rotational lightcurve of Medesicaste was first obtained by Stefano Mottola in November 1991, using the Loiano 1.52-meter telescope at Bologna Observatory in Italy.

[9][13] Since January 2015, several photometric observations by Robert Stephens at the Center for Solar System Studies in California confirmed Mottola's period determination from 1991, and measured a brightness amplitude of 0.50–0.53, which is indicative of a non-spherical, possibly elongated shape (U=3-/3-/3).