The two-week excavation, which began last week, is now being extended by an extra seven days, following the discovery. Pete Boland, Dudley Council's borough archaeologist, said records suggested that a glass cone was built on the site in the 1700s and that was what had been found.
"This in itself is a major discovery and is an important addition to the town's incredible history," he said.
"Even better we have uncovered part of the furnace that would have occupied the centre of the cone.
"It is well preserved and we are taking the opportunity to uncover it fully to analyse it in more detail.
"This requires the dig to be extended for a number of days and will mean the car park is closed for a little longer.
"However, I am sure everyone will understand the need to record this find before the ground is prepared for the construction of the new public square."
The cone and furnace are being cleaned ready to be studied. Experts are also hoping to unearth more history of the Stone Street area before it is developed into a new town square.
"These finds have given us a new insight into how the cone was constructed ," said Mr Boland.
Alternative car parking can be found in Stafford Street, Priory Road and Flood Street. The car park will re-open on February 3.