The latest fatality occurred in the city of Almeria, where a man drowned when his car became trapped in a tunnel, the AFP news agency reported.
A tweet from Almeria city hall revealed that the tunnel was "flooded by a huge amount of water in a few minutes," AFP said.
Spanish Prime Minister Pedro Sanchez said in a tweet that it was "a hard and difficult night. Several locations remain on alert for torrential rains. We sadly regret a third fatality in Almeria."
The latest death follows those of two siblings on Thursday -- a 61-year-old man and his 51-year-old sister died when their vehicle was swept away by fast-moving waters in Caudete, about 60 miles southwest of Valencia, AFP reported, citing the emergency services.
Flash flooding is causing widespread road closures and serious disruption to public transportation.
The closure of local train networks, dozens of roads and the airports in Almeria and Murcia has led to long delays, according to Spanish airport operator Aena.
"These adverse weather conditions affect the airports of Almera, Josep Tarradellas Barcelona-El Prat and Palma de Mallorca. Check the status of your flight with your airline."
Authorities have urged members of the public to stay at home where possible, and schools across the region have suspended classes, according to AFP.
Meanwhile, the news agency reported emergency services as saying that some 60 people were rescued early Friday from a campsite in the Cabo de Gata nature reserve on the coast of Almeria.
There is a further "risk of loss of life," as well as "damage to property and infrastructure," a spokeswoman for Britain's Met Office weather service told CNN.
"Thunderstorms will continue across eastern Spain and the Balearics for the remainder of this week, but we expect that things will start easing off by Sunday," she said.
Britain's Foreign & Commonwealth Office advised those traveling to the regions to "exercise extreme caution and follow the advice of the local authorities."