Margaret McGinnes, 79, was crossing Old Edinburgh Road in Uddingston at around 9.30am on Friday when she was hit by a blue Vauxhall Astra.
Emergency services attended and Ms McGinnes was taken to Wishaw General Hospital for treatment but later died.
Her family are aware and a report is to be sent to the Procurator Fiscal.
Constable Jim Dewar said: “We are appealing to anyone who may have noticed a blue Vauxhall Astra driving on or near to Old Edinburgh Road on Friday morning to get in touch.
“Anyone with information is asked to contact the Divisional Road Policing Unit based at Motherwell via 101, quoting incident number 0958 of Friday 25 May 2018.”