John Degenkolb, Warren Barguil, Chad Haga, Fredrik Ludvigsson, Ramon Sinkeldam and Max Walscheid were all taken to hospital in Alicante and are said to be in a stable condition.
"During the training ride, a car coming the other direction rode into the group of riders head on. The riders were riding side by side on their own side of the road," Giant-Alpecin said in a statement.
The English female driver of the car was on the wrong side of the road when the accident occurred according to the emergency services.
"Everyone on the team is in shock right now, and there are some major issues that we need to take care of, but we also realise that we have had some luck on our side," said team physician Anko Boelens.
"Everyone is conscious, stable and approachable, but we are waiting for the latest information and consult the doctors in those hospitals about the treatments needed for the riders."
One of the riders was reported as seriously injured, but his condition is not life threatening.
"The cyclist has functional injuries of a severe nature, but in principle they don't implicate any risk to life," said a hospital source.
In 2012 Spanish cyclist Victor Cabedo was killed after being run over on a training run in Almedijar near Valencia.