The fire broke out at The Village Plaice, a two-storey building on High Street.
The road has been closed off while crews work at the scene. An ambulance and paramedic officer were called by the fire service at 11.51am and assessed two women for smoke inhalation, who were later discharged at the scene.
A number of firefighters were wearing breathing apparatus to tackle the blaze.
Fire crews were called at 11.03am to the fire.
Three engines were sent, along with a four by four brigade response vehicle, and crews began to dampen down at 12:05pm.
Some smoke has affected two neighbouring properties, including a Cantonese restaurant.
A staff member at local hair salon Nicholas Davis Hair and Beauty said: "We are all OK. We did see the fire, there was lots of smoke but it didn't reach us."
Another witness described the chip shop as "gutted" by the blaze.
⚠️Service Disruption⚠️— NX West Midlands (@nxwestmidlands) November 29, 2022
Building fire on High Street, #Tettenhall
🚌62/A diverted towards #Wolverhampton via:
Church Road, School Road, The Crescent, Woodhouse Road North, Regis Road and The Rock
No service on Wood Road or High Street
Apologies for any inconvenience caused
A spokesman for West Midlands Fire Service said: "The incident, involving a chip shop fryer on the ground floor of a two-storey building, has been extinguished by fire crews using a hose reel jet operated by firefighters wearing breathing apparatus.
"The fire is now out and crews are damping down and cutting away and are monitoring the scene.
"There was smoke logging to adjacent commercial properties, which has been cleared by firefighters.
"One female suffered smoke inhalation. The owner of the property is in attendance and is liaising with our crews."
National Express West Midlands was forced to divert services to Wolverhampton, including bus 62/A.