The 78-year-old woman has sustained life-threatening head injuries.
“The woman was operated on yesterday evening at the neurosurgery clinic in Lund and her condition was serious, and remains serious on Tuesday morning,” Hans Boklund at Skåne University Hospital told news agency TT.
Police had found no trace of the assailant by late Tuesday morning.
“We have got in a whole load of tips and witness testimony, but we need more,” said Cindy Schönström-Larsson at Skåne police.
Police received a report over the hit and run attack in front of the Hemköp supermarket in central Landskrona at around 2pm on Monday.
The woman, who is from the Swedish town on the south-west coast, was punched in the face when she tried to intervene to protect her soon 80-year-old husband.
According to Skåne police, the assailant is a young man aged between 20-30, who fled the scene in a small red car – either a Mazda or a Toyota.
The aggravated assault occurred after an exchange of words in connection with a parking situation, where the elderly man had sounded his horn in order to get the younger man to move his car.
After the older man had parked his car, the young man challenged him over why he had sounded the horn. He opened his door, hitting the elderly man as he passed by and pushing him onto the bonnet of a nearby vehicle. The young man then punched him on the back and in the face, according to Persson.
“That’s when the woman tries to intervene. She is then punched in the face and knocked out.”