North Yorkshire Police said the shocking incident happened in High Petergate at 10pm on Saturday, January 27.
The woman, in her 50s, received a small cut to her knee while the man, aged in his 20s, suffered a bruise on his face, police said.
Another woman in her 20s, who was with the man and woman, did not suffer any injuries.
A police spokesperson said: “We are requesting the public’s assistance to help establish the full circumstances surrounding the incident.”
Anyone with information that could assist the investigation is asked to email joanne.bell@northyorkshire.police.uk in the York Initial Enquiry Team. You can also call North Yorkshire Police on 101, select option two, and ask for Joanne Bell.
If you wish to remain anonymous, you can pass information to Crimestoppers on 0800 555 111.
Please quote the North Yorkshire Police reference number 12240016641.
