Galtier was taken to hospital on Tuesday following a fall that resulted in him striking his head on a metal goal he was carrying.
The 47-year-old suffered a laceration to his face, with reports suggesting that Galtier had been unconscious for around three minutes.
However, despite the severity of the incident, Saint-Etienne revealed that hospital scans had eased fears over the seriousness of Galtier's injuries.
"This morning, after the workout, Christophe Galtier slipped on the ground carrying a metal mini goal," a statement on the club's official website read.
"The coach of ASSE, whose head hit the goal, suffered a head injury which resulted in a loss of consciousness.
"Suffering from a deep wound in the right cheekbone, he was immediately supported by the medical staff of the club and then by firefighters and ambulance personnel.
"Additional tests performed at the hospital proved reassuring."
Champions League chasers Saint-Etienne travel to Toulouse on Friday and will move into third place in Ligue 1 if they avoid defeat.