Raging flood waters swept through the town of Letur in the eastern province of Albacete, pushing cars through the streets, images broadcast on Spanish television showed, AFP reported.
Emergency services workers backed by drones were looking for six people who were missing in the wake of flash floods in the town, the central government's representative in Castilla-La Mancha, Milagros Tolon, told Spanish public television station TVE.
"The priority is to find these people," she added.
Police in the town of L'Alcudia in the eastern region of Valencia said they were looking for a truck driver who has been missing since the early afternoon.
"I am closely following with concern the reports on missing persons and the damage caused by the storm in recent hours," Prime Minister Pedro Sanchez wrote on X, urging people to follow the advice of the authorities.
"Be very careful and avoid unnecessary trips," he added.
Twelve flights that were due to land at Valencia airport were diverted to other cities in Spain due to the heavy rain and strong winds, Spanish airport operator Aena said.
Another 10 flights that were due to depart or arrive at the airport were cancelled.
Valencia city hall said all school classes and sports events were suspended on Wednesday, and parks would remain closed.
National rail infrastructure operator ADIF said it had suspended all rail services in the Valencia region "until the situation returns to normal for the safety of passengers".
High-speed trains between Madrid and the city of Valencia will be suspended until "at least" 10 am on Wednesday due to the effects of the storm, it added.
A high-speed train with 276 passengers derailed in the southern region of Andalusia, although no one was injured, the regional government said in a statement.
Emergency services rescued scores of people in Alora in Andalusia, some by helicopter, after a river overflowed.
State weather agency AEMET declared a red alert in the Valencia region and the second-highest level of alert in parts of Andalusia. Several roads were cut in both regions due to flooding.
Scientists warn that extreme weather such as heatwaves and storms is becoming more intense as a result of climate change.