The 29-year-old officer, who suffered a leg injury, had been carrying out inquiries in Ness Drive at about 20:30 on Wednesday when the Audi 4 hit him.
The car was later traced and a 38-year-old man was arrested. He is expected to appear at Hamilton Sheriff Court on Friday.
The police officer is in a stable condition in Hairmyres Hospital.
A police officer is being treated in hospital after a car was allegedly driven at him in East Kilbride.