This is an example of an urban legend that may have its roots in truth.

This is L'Arrivée d'un train en gare de La Ciotat (The Arrival of a Train at La Ciotat Station), filmed by the Lumière brothers in 1895. It was filmed in one continuous shot that showed a train pulling into a station. The extent of the audience's reaction is in dispute, but everyone seems to agree that the first audience that saw it was visibly effected by what they saw.

In his 1962 book History of Film, Ulrich Gregor says:

"...according to handed-down knowledge, the locomotive terrified the audience."

Film critic Lotte H. Eisner recalls in 1983:

"...the spectators in the Grand Café involuntarily threw themselves back in their seats in fright, because Lumière's giant locomotive pulling into the station seemingly ran toward them."

On the centennial celebration of the film's release, film critic Hellmuth Karasek wrote in Der Spiegel:

One short film had a particularly lasting impact; yes, it caused fear, terror, even panic....It was the film L'Arrivée d'un train en gare de la Ciotat (Arrival of the Train at La Ciotat Station)....Although the cinematographic train was dashing toward the crowded audience in flickering black and white (not in natural colors and natural dimensions), and although the only sound accompanying it was the monotonous clatter of the projector's sprockets engaging into the film's perforation, the spectators felt physically threatened and panicked.

The German Railway's customer magazine then picked up the story and ran with it:

"The spectators ran out of the hall in terror because the locomotive headed right for them. They feared that it could plunge off the screen and onto them."

Soon thereafter The Munich Abendzeitung leapt onto the bandwagon saying:

"...at the time, people, appalled by Arrival of the Train, were said to have leaped from their chairs."

Today all of these claims are generally regarded as rumor. While it certainly could have happened, there are no contemporary sources available to back up the story of the panic caused by seeing a moving train on a screen.

Source:

Lumière's Arrival of the Train: Cinema's Founding Myth by Martin Loiperdinger. From The Moving Image Volume 4, Number 1, Spring 2004