It was discovered on 3 June 1875, by German–American astronomer Christian Peters at Litchfield Observatory of the Hamilton College in Clinton, New York, United States.

[18] Peters named it after Vibilia, the Roman goddess of traveling, because he had recently returned from a journey across the world to observe the transit of Venus.

13-cm radar observations of this asteroid from the Arecibo Observatory between 1980 and 1985 were used to produce a diameter estimate of 131 km.

[7] According to the surveys carried out by the Infrared Astronomical Satellite IRAS, the Japanese Akari satellite, and NASA's Wide-field Infrared Survey Explorer with its subsequent NEOWISE mission, Vibilia measures between 131.36 and 142.38 kilometers in diameter and its surface has an albedo between 0.05 0.06.

[5][6][9][8] The Collaborative Asteroid Lightcurve Link (CALL) adopts the results obtained by IRAS, that is, an albedo of 0.0597 and a diameter of 142.38 kilometers.

Lightcurve analysis gave a rotation period between 13.810 and 13.88 hours with a brightness amplitude between 0.13 and 0.20 magnitude (U=3/3/3/3).