The officer, named in media reports as Greg McDougall, was trying to talk to a man in his ute in Belmont on Friday afternoon when the driver allegedly sped away, striking him.
Mr McDougall was rushed to Royal Perth Hospital with critical injuries, prompting Premier Roger Cook label the incident as "simply not acceptable".
A 37-year-old-man was charged on Saturday with driving-related offences over the alleged hit and run.
On Monday, the officer's brother Chris McDougall said his condition "was touch and go on Friday night".
He said his brother needed blood transfusions after suffering broken ribs, a broken arm and fractured ankle while on duty.
"That was our biggest concern, Friday night, getting through the night," Greg McDougall said in Seven News footage.
"He's so strong, every time we saw him he always gave us the thumbs up.
"He's so tough, he's superman to most of the family, he really is."
Mr Cook on Saturday said he understood the incident was "unrelated to any organised crime activity".
"It is simply a matter of an officer trying to execute an arrest," he said.
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