The incident occurred on Saturday night with the patient approaching a nurse in a corridor, stepping on her foot and then punching her in the head.
The 75-year-old man, who was waiting to be transferred to a specialist aged care unit, chased staff around the ward, with two nurses and three doctors suffering minor injuries including bruising.
SA Health said all staff had returned to work following medical assessments.
"We have a zero tolerance for violence and aggression at our sites and our priority is to provide a safe environment for staff, patients and visitors at our hospitals," SA Health said in a statement.
"The incident that occurred at the weekend is unacceptable and we acknowledge the impact for staff involved."
Individual and group counselling sessions have been organised.
SA Health said a number of measures had also been implemented to improve safety while a security working party was conducting a full investigation to develop an appropriate response, including de-escalation training and the provision of duress alarms for all staff.
SA police said patrols were called to the hospital four times on Saturday to assist with the patient but no charges were laid.
The Australian Nursing and Midwifery Federation said the incident was the latest in a series of attacks at country hospitals.
"Saturday's harrowing incident follows a spate of recent violent episodes at regional hospitals where there are no 24/7 restraint-trained security guards to protect staff, patients and visitors,'' federation chief executive Elizabeth Dabars said.
The union said in February that a man had to be tasered four times by police after smashing multiple glass panels at Wallaroo Hospital terrorising staff and patients.
"We know from a review into hospital safety in Port Augusta and Whyalla last year that the presence of 24/7 security guards has had a very positive impact not only in terms of reducing violent incidents but also in alleviating the psychological stress on staff,'' Ms Dabars said.
The union urged the SA government to implement other measures to improve safety, including extra education and training for health workers.
Lifeline 13 11 14
beyondblue 1300 22 4636
