Police said officers were called to a disturbance at the Paralowie address at about 5.35am (CST) this morning.
When the officers approached the house they were shot at, through the front door.
A spokeswoman said both suffered shrapnel wounds that were not life-threatening.
One was taken to the Lyell McEwin Hospital and the other to the Royal Adelaide Hospital.
The spokeswoman said a siege developed with the gunman taking to the roof of the house as elite STAR Group officers and police negotiators were called in.
After a short while the man surrendered and was arrested.