Aurier, 27, shared three images on Instagram of himself in a chair on Tuesday night, in front of his barber with a caption "Yes Sir" and a hashtag Le CoiffeurEstBon, which translates as "the 'hairdresser is good."
Aurier also tagged the account of Justin Carr -- a hairdresser who counts Liverpool midfielder Alex Oxlade-Chamberlain and Manchester City's Kyle Walker among his clients -- but it is unclear when the pictures were taken.
The defender responded to reports of his breach in an Instagram post that read: "My hairdresser is negative and me too so stop talking in a vacuum and put on masks and gloves when you come to take pictures at the training center it's part of the rules too."
A Spurs spokesman told ESPN: "We are investigating the circumstances and will deal with the incident appropriately."
The club are likely to take a dim view of Aurier's actions, given he has twice been warned about his conduct during lockdown.
Spurs returned to "Phase 1" training Wednesday as the Premier League edges toward a possible restart. Spurs began group sessions of no more than five players for the first time, with Aurier in attendance, as planned.
Aurier was tested as part of a leaguewide programme on Tuesday that yielded only six positive results from 748 players and staff.
If Spurs discover this latest incident came after that test, Aurier could be asked to self-isolate for seven days.