The first modern disaster was the Lisbon earthquake of 1755. Modern because it was the first disaster not attributed to the supernatural, but to the natural and it was the first disaster involving a coordinated state disaster relief.
According to Russell Dynes, "...of particular interest here are the circumstances which led to the earthquake being attributed to 'natural' rather than 'supernatural' causes. Before that, men traditionally interpreted earthquakes as a dramatic communication between gods and humans. In particular, such events previously had been explained as indicating some disturbance between earthly and heavenly spheres. The Lisbon earthquake can be identified as a turning point in human history which moved the consideration of such physical events as supernatural signals toward a more neutral or even a secular, proto-scientific causation."
This disaster was not the most deadly in history but it had a profound impact on Europe. "Depictions of the earthquake in art and literature can be found in several European countries, and these were produced and reproduced for centuries following the event, which came to be known as 'The Great Lisbon Earthquake.'" (The Earthquake Engineering Online Archive)
The significance of the Lisbon Earthquake was that it was the beginning of modern seismology. Following the 1755 Lisbon earthquake, an effort to catalog the times and locations of earthquakes and to study their physical effects began.
More References
For more information about this natural disaster that changed the world, check out these resources on the topic.
Earthquake at Lisbon, 1755
From the Modern History Sourcebook website, you can read the first-hand account of the event by the Rev. Charles Davey.
Earthquake of Lisbon 1755
From the Earthquake Museum website, you can read about the earthquake and its aftermath.