The incident happened shortly before 1.50am on Monday in Lyth Hill Road, Bayston Hill.
Police were called and the driver, a man in his 30s, was arrested on suspicion of drink driving.
Paramedics attended the scene and the man was taken to Royal Shrewsbury Hospital with minor injuries.
The vehicle was travelling south down the road before it crashed into a telegraph pole and then destroyed the front porch and wall to a nearby property.
The smash snapped the bass of the pole and moved it about 4ft up the road, leaving it hanging on by power cables near to the turning for Lodge Crescent.
Western Power Distribution (WPD) confirmed 49 properties in the area were left without power, and said it hoped to restore electricity to the final 11 homes by 11.30am.
Engineers were on site throughout the morning to make the area safe.
The road was closed from its junction with the A49 to Lythwood Road, with a diversion taking motorists via Cross Roads.
Shropshire Fire & Rescue service sent one appliance from Shrewsbury Fire Station following the crash and reported that "one vehicle came to rest into property".
An operations officer was in attendance and crews were at the scene for about 40 minutes while the wreckage was cleared.
A West Mercia Police spokesman said: "Police attended a road traffic collision between a car and a telegraph pole at around 2am on Monday, July 12. A man in his 60s was arrested at the scene for driving with excess alcohol."
A spokeswoman from West Midlands Ambulance Service said: "We were called at 1.48am to reports of a car which had collided with a house in Lyth Hill Road, Bayston Hill, Shrewsbury. An ambulance and a paramedic officer attended and treated one man, the driver of the car, who had sustained minor injuries. He was conveyed to Royal Shrewsbury Hospital for further checks."
A WPD spokesman said: "I can confirm there was a fault due to damage to a pole by a vehicle this morning. There were 49 properties without power due to this. We have 11 properties still without power at present with an estimated time of 11:30am for restoration."