The lorry belongs to Chilton Bulk Transport based in Abertillery, South Wales, which was transporting glass to North Wales.
Boss Steven Chilton said: “The last I heard was that he’d broken his leg. I’m waiting for an update from the hospital.
“This is the first time we’ve had anything like this happen so it’s a bit of a shock to the system.
“I don’t think this driver has ever had an accident working for us. He’s been with us five years, possibly going on 10.”
Asked how much the collision is likely to cost the company, Mr Chilton said: “I don’t want to think about that, it’ll just make me ill.”
Shropshire Fire and Rescue Service said three fire engines attended and crews used cutters, spreaders, small gear and ladders to deal with the incident.
A spokesman said: “At 5.29am on Monday, November 11, SFRS Fire Control received a call reporting that a road traffic collision had taken place in Shrewsbury.
“One lorry in collision with two buildings. One casualty released from vehicle by fire service personnel using cutting equipment.
“A49 is currently blocked at Bayston Hill by attending emergency service vehicles. Road users should seek alternative routes until further notice.”
A post by National Highways West Midlands on X said: “Traffic is held on the #A49 southbound between #A5 #A5112 (at Dobbies Island near #BaystonHill #Shrewsbury (south) and #B4371.
“A lorry has left the carriageway and hit a building. @OPUHereford & @HWFireControl are in attendance. Updates to follow.”
West Mercia Police and West Midlands Ambulance Service were also in attendance.
