The limb was found in a garden in Cranwells Park on Wednesday and has been sent for forensic analysis, Avon and Somerset Police said.
A force spokesman said detectives were "keeping an open mind" as to whether it was linked to two similar incidents in the city.
All three feet have been found within a few hundred yards of each other.
Tests showed the first foot found in Weston Park East in February was  "probably" a medical teaching aid. The second foot, found last month in the same area, is still undergoing tests.
"The same officers are looking into the latest discoveries and will look to confirm beyond all reasonable doubt that they are linked and if there are any new lines of inquiry which can be taken forward," the spokesman added.
A third human foot has been found close to where two others were discovered earlier this year.