According to the StarCraft wiki, the use of large-scale nuclear weaponry was banned in the late 2490s due to their (mis)use in quashing the Rebellion of Korhal:
The colonists of Korhal IV rebelled against their former masters, the Terran Confederacy. The latter resorted to assassinating its first leader with ghosts but still failed to control the rebellion. The Confederacy resorted to firing a thousand Apocalypse-class nuclear missiles at Korhal from the distant Confederate capital of Tarsonis, killing four million people and destroying most life on the planet and setting the forests on fire.
After the Korhal incident, full-scale use of nuclear weapons were banned on habitable worlds. The Confederacy began using smaller missiles, targeted by ghosts
RavenDreamer also found this from the SC1 manual:
Although our typical image of a nuclear weapon is something that obliterates a large area, tactical nuclear devices exist today, and were deployed as far back as the 1960s during the cold war. Although nuclear weapons generally produce a much larger and more devastating/deadly explosion than conventional bombs, there are conventional bombs with more explosive force than the smallest nuclear weapons.
Theoretically, a bomb launched from a silo and laser guided to a ground target could do damage consistent with the StarCraft nuke, although I do not believe this has ever happened in a war scenario.