288 Glauke is a stony, tumbling asteroid and slow rotator from the intermediate asteroid belt, approximately 32 kilometers in diameter. It was discovered on 20 February 1890, by Robert Luther at Düsseldorf-Bilk Observatory in Germany. This was the last of his asteroid discoveries. It is named after Creusa (known as Glauce or Glauke), a daughter of Creon, a king of Corinth in Greek mythology.

This body is orbiting the Sun at a distance of 2.76 AU with a moderate eccentricity of 0.20 and an orbital period of 4.59 years. Its orbital plane is inclined at an angle of 4.3° relative to the plane of the ecliptic. It is a common, stony S-type asteroid in both the Tholen and SMASS classification. Based on infrared observations, it has a diameter of 29 km.

Glauke has an exceptionally slow rotation period of about 1200 hours (50 days). This makes it one of the slowest-rotating asteroids in the Solar System. The rotation is believed to be "tumbling", similar to the near-Earth asteroid 4179 Toutatis.