Born in Groningen in the Netherlands, Schmidt graduated from the university there in 1949 and obtained his PhD in 1956 from Leiden University. After working at the Leiden Observatory from 1953 to 1959, he moved to America, taking up an appointment at the California Institute of Technology as a staff member of the Hale Observatories. He was made professor of astronomy in 1964 and also served as director of the Hale Observatories from 1978 to 1980.

Schmidt has investigated the structure and dynamics of our Galaxy and the formation of stars but he is best known for his research on quasars, or quasi-stellar objects. In 1960 Alan Sandage and Thomas Matthews identified a compact radio source, known as 3C 48, with a 16th-magnitude starlike object that was found to have a most curious spectrum. Soon, other optical identifications were made, including that of 3C 273 with a 13th-magnitude object that had an equally puzzling spectrum. These objects became known as quasars. In 1963 Schmidt was the first to produce a satisfactory interpretation of the spectrum of a quasar.

Schmidt realized that certain broad emission lines in the spectrum of 3C 273 were the familiar hydrogen lines but shifted in wavelength by an unprecedented amount. According to the Doppler effect, light emitted from a source that is moving away from an observer increases its wavelength, i.e., its spectral lines shift toward the red end of the spectrum. The faster an object is moving away, the greater the so-called red shift. Hubble had assumed that the red shift of the galaxies was explained by the Doppler effect: the galaxies were receding as the universe expanded and that as the velocity and hence the distance of a galaxy increased, its red shift increased accordingly. 3C 273 had an immense red shift. Assuming it to be a Doppler shift resulting from the expansion of the universe, Schmidt was amazed when he found that 3C 273 must be a billion light-years away. In that case, how could such a small source be visible at such an enormous distance? It would need to be as luminous as a hundred galaxies and it was by no means clear what physical mechanism could yield so much energy from such a compact source. Schmidt's work was soon confirmed by the red-shift interpretation of the spectra of other quasars; they all possessed unusually large red shifts. There arose a long debate as to whether the Doppler effect did explain the quasar red shift but it is now generally accepted that this is the case.

By the end of the 1960s many quasars had been discovered and their distribution mapped in the heavens. Schmidt realized that this allowed him to test the cosmological steady-state doctrine of Thomas Gold and others, which assumes that the universe on a large scale looks the same at all times and all places. He found, however, on examining the distribution of quasars and using the Doppler interpretation of their red shifts, that their numbers increase with distance and that they are indeed the most distant objects in the universe. Assuming that the big-bang rather than the steady-state theory is correct, they are also the youngest objects in the universe.

The discovery of the quasars with the problems they posed produced an enormous growth in astronomical research that led to the discovery of even stranger objects, such as pulsars, and the continued search for black holes. Huge black holes are indeed thought to be the source of the prodigious energy of quasars.