They revealed, in a tweet: "The A30 has been closed because a lorry has overturned. Elephants are loose on the tarmac.
"The motorway has been closed around the Pozo Canada area heading towards Murcia."
The accident is believed to have happened after the HGV they were in overtook another vehicle and the driver lost control as he headed back into the slow lane.
Spain's Road Safety Authority the DGT confirmed one of the elephants had died in the incident.
Four other animals escaped the crash with their lives along with the driver of the vehicle.
Two of the four-legged survivors are said to have suffered injuries although it was not immediately clear how serious they were.
DGT spokesman Gregorio Serrano said: "The elephants injured in the accident that has happened in Albacete are being assisted and removed.
"Of the five animals one has died and two have been injured. Shortly the A30 will be reopened."
One stunned motorist, who filmed the animals wandering around on the tarmac seconds after the accident, said in a running commentary over his home-made video: "Accident on the A30 motorway near Albacete.
"A circus lorry has overturned. Four elephants are loose and one looks in a very bad way. I'm not sure if it's dead or not."
Silvia Barquero, the president of Spanish animal welfare political party PACMA, said the animals belonged to the Gottani Circus, which has performed several shows in the area over Easter.
She tweeted: "The lorry that has overturned was carrying Circo Gottani elephants. Show them more kindness. We treat animals like slaves. Enough of circuses that use animals."
There was no immediate response from the circus owners.
Civil Guard officers will now send a report on the accident to a local investigating judge who will be tasked with a routine probe into the incident.