The 33-year-old man was held in connection with the incidents in Cambuslang, South Lanarkshire, on Friday night.
The 44-year-old male driver was assaulted in Eastfield Avenue at about 7.50pm. A short time later, a 68-year-old woman was attacked in the town's Dukes Road.
Both the driver and the woman were taken for treatment to Hairmyres Hospital in East Kilbride, where it is understood they remain.
Police Scotland said: "A 33-year-old man has been arrested and is presently detained in police custody in connection with alleged assaults on a 44-year-old man and 68-year-old woman in Cambuslang on Friday June 20."
He is expected to appear at Glasgow Sheriff Court later.
A report is being sent to the procurator fiscal.