The incident happened in Lyth Hill Road, Bayston Hill, shortly before 1.50am on Monday.
The driver - whom police originally described as being in his 60s but later said is in his 30s - was arrested on suspicion of drink driving and has been released pending further investigations.
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 base 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.
Forty-nine properties in the area were left without power following the crash.
Western Power Distribution has since confirmed some customers were put on temporary generators while the telegraph pole was replaced.
Engineers worked throughout the day and all supplies are now restored.
Paramedics attended the scene shortly after the incident and the driver was taken to Royal Shrewsbury Hospital with minor injuries.
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.