The finds, which include massive walls and what appears to be a stairway entry, were confirmed using a state-of-the-art ground-penetrating radar.
Historian and Northampton resident, Marcus Roberts, who is director of National Anglo-Jewish Heritage Trail (JTrails), said: "We've been working in partnership with Birmingham University and we were able to get a ground penetrating radar to do a survey of the site.
"We found what would appear to be the remains of a substantial masonry walls under the cellar walls of Kebabish. It also showed what appears to be two walls 3 feet in width and going down 14 feet underneath cellar level.
"There was also a square or rectangular structure next to it which may well have been a stair well going down into the synagogue."
Last year, an archaeological survey of what is now Lawrence Court, in Northampton, discovered what historians think is the site of a 12th century Jewish cemetery and evidence of a further group of burials close to those first discovered in 1992, after JTrails Director, Marcus Roberts, predicted the presence of the cemetery in Temple Bar.
Mr Roberts, who is leading the search with Caroline Sturdy Colls, a PhD archaeology student at Birmingham University, and a geophysics and forensic specialist, warned he could not be certain what the latest finds were without excavating the site.
However, he said all the historical records suggested Sheep Street was once home to a medieval synagogue and that this precise location adjacent to the former Fish Market was most likely to be the site of the synagogue with other Jewish houses around it and the that the former synagogue may have survived to at least as late as 1674 and the Great Fire of Northampton.
Mr Roberts said: "I have looked through all the possible documentary sources for this and my research led me to conclude that this area of Sheep Street was where we would have found the Jewish properties in medieval Northampton and which are listed in medieval rentals for the town.
"We cannot say conclusively this is the synagogue.
"But we thought we would find the synagogue there and what we have found is an extremely substantial medieval sunken building. Medieval synagogues in England were usually sunken into the ground"
Mr Roberts says the discovery, which was made possible thanks to the co-operation of the shop owners and Northampton Borough Council, could also prove to be of national importance.
He said: "There are so few of these things around.
"There are very few remains of medieval synagogues in this country.
There have been some structures that have been destroyed and apart from one structure recently discovered in Guildford there are no other medieval synagogues structures that I know of in England,though some historians believe that an upper room at Jew's Court at Lincoln may have been used for worship before 1290."
• Last Updated: 09 April 2010 12:27 PM
• Source: Northampton Chron & Echo
• Location: Northampton