Smoke billowed from the roof and all the windows across the second and third floors of the former Corbet Arms Inn building on High Street at 6.30pm on Wednesday.
The blaze ravaged the upper levels of the Post Office, which remains shut, and its cause is still under investigation by specialist officers.
High Street and Stafford Street were closed as a large presence of emergency services worked to control the fire.
Shropshire Fire & Rescue Service sent six appliances from Hodnet, Market Drayton, Newport, Prees and Whitchurch, and were supported by crews from Staffordshire Fire & Rescue Service's Loggerheads base.
West Mercia Police (WMP) was also at the scene.
After battling the blaze for more than two-and-a-half hours, thee fire service confirmed that no one was injured.
A statement from the Post Office said: "We as a team would like to thank you all for your concern and kind words.
"The Shah family, Vicky Jones and Melissa Leanne are all safe. We are waiting on a damage report right now; as soon as we know how bad the damage is and if we can open or not we will let you know.
"We pray and hope that no one else was hurt, and that the damage is small."
A spokesman from Market Drayton Fire Station said: "On arrival at the scene the Market Drayton crew was confronted with smoke issuing from the roof and all the windows across the second and third floors of the old Corbet Arms hotel – a Grade II Listed building.
"The crew was faced with a very challenging incident involving a large complex three-storey building, an unknown location and size of fire and multiple locked and boarded up entry points.
"The decision was made to commit two firefighters wearing breathing apparatus into the first floor of the building, taking with them a high pressure hose reel jet to try and locate and extinguish the fire.
"On arrival of the supporting appliances and crews, the number of firefighters committed into the building wearing breathing apparatus was increased to six, with an additional three high pressure hose reel jets and a main jet being got to work.
"While the breathing apparatus crews were working in near-zero visibility in places to locate and extinguish the fire, other crews were establishing an additional water supply from a nearby fire hydrant, as well as pitching a 13.5m ladder to the third floor windows to allow for inspections to be carried out.
"Officers from WMP were urgently requested to attend to assist with traffic control, which resulted in High Street and Stafford Street being closed.
"The breathing apparatus teams, working in hazardous conditions which included holes in the floor, located a severe fire on the first floor of the building, which involved a large quantity of scrap wood, building debris and wooden flooring."