The attack happened as the 22-year-old man walked along the footpath through Greenfields Gardens near Ellesmere Road and the Wood Street junction in Shrewsbury.
He was treated in hospital after sustaining serious lacerations to the face.
The dog has been described as a large orange and black Alsatian and may be dangerous.
Police are asking for anyone with information about the attack to come forward and contact police on the non emergency number 101 quoting incident number 477s of 12 June.