The fire, which broke out in Ashbourne Road at around 5am on Tuesday, is believed to have started in the living room of the two-storey house and then damaged half the building, with smoke also spreading next door.
Fire crews from Bloxwich, Walsall and Willenhall, along with paramedic officers from West Midlands Ambulance Service, arrived to find a man from the burning house with burns and a next-door neighbour suffering effects of smoke inhalation.
The man was taken to Walsall Manor Hospital for further treatment, while the woman was discharged at the scene.
A spokesman for West Midlands Ambulance Service said: "We were called to reports of a house fire on Ashbourne Road, Bloxwich, at 5.23am.
"One ambulance and two paramedic officers attended the scene. On arrival we discovered two patients, one of whom, a man, was treated for burns before being taken to Walsall Manor Hospital.
"The second patient, a woman, was treated for the effects of smoke inhalation and discharged on scene."
A spokesman for West Midlands Fire Service said: "We were called to reports of a house fire at a terraced property on Ashbourne Road in Bloxwich around 5.12am.
"Four crews from Bloxwich, Walsall and Willenhall responded with 20 firefighters in total, with the first engine arriving on the scene four minutes after the call.
"They used hose reel jets and breathing apparatus to tackle the fire, which is believed to have started in the downstairs living room and broken through to the first floor.
"A man who is believed to be in his 70s managed to get out of the property and our crews gave him oxygen therapy before he was released into the care of the ambulance service and taken to hospital.
"A woman from a neighbouring property was also affected by smoke inhalation and given oxygen treatment by our crews and discharged at the scene."