The sneak in theft happened last night between 5.30pm and 7.30pm in Oakley Street, Belle Vue.
Police are seeking witnesses who were in the area at the time and might have seen someone acting suspiciously.
Constable Tony Smith, the investigating officer, said: “The occupants were in the front room and didn’t see or hear anything. The offender sneaked in through a door and took the money and a credit card from the kitchen.
“Anyone who can assist the investigation is asked to contact Shrewsbury police station on 101. Information can also be given to the anonymous Crimestoppers number, 0800 555 111.”