They suspect he could have cut himself while fleeing from a flat in Camross Drive, Herongate after being disturbed by the occupants during the early hours of yesterday.
The intruder, who is described as white and about 5ft 8ins tall, wearing a balaclava over his face and dark clothing, entered the flat between 1.30am and 2am. He disturbed a woman who raised the alarm after being awoken.
Detective Inspector Pete Brophy, in charge of the burglary unit at Shrewsbury police station, said: “We believe he may have suffered a cut and as a result are carrying out extensive forensic work as part of our investigation.
“We are appealing for witnesses to this incident or any information which might help identify the man involved.
“In particular, if anyone saw suspicious activity in the Camross Drive area at around 1.30am or 2am yesterday, such as a man running, do contact Shrewsbury police on 101.”
Information can also be given to the anonymous Crimestoppers charity by calling 0800 555 111, for which a reward may be paid.
Nothing was stolen during the incident.