According to the Media Guardian, Tucker had been chief executive Murdoch MacLennan's second-in-command since joining in March last year, following the departure of managing director John Allwood.
The resignations come as TMG continues to bicker with Express Newspapers over its departure from the Westferry print site on the Isle of Dogs.
Tucker, who was a director at West Ferry printers, as well as one of seven board members at TMG, has quit after just 14 months in the job.
He follows marketing director Katie Vanneck and new media director Shaun Gregory.
Tucker has previously held a director's post with St Ives printing group.
According to the Media Guardian, TMG did not wish to comment on the departure.
Finance director becomes latest to quit in TMG crisis
The Telegraph Media Group (TMG) has lost another key member of staff with the resignation of finance director Simon Tucker last week.
