Tavecchio has denied the claims. "In relations to what has been reported in some press articles, I maintain that I behave in a correct manner and in order to protect my image and honour I have asked my lawyers to act in the appropriate forums," he told ANSA news agency.
The woman, given the pseudonym "Mary" by Milan daily Corriere della Sera described an encounter with Tavecchio in his office at the federation's headquarters in Rome.
"I went into his office to talk about football," she said. "He did not even give me time to ask 'president, how are you?' He looked at me and said: 'You look well, I can see you have an active sex life.' Then he said: 'Come here and let me touch your breasts.'
"I was embarrassed. I tried to tell him to stop. But his only answer was to close the curtains of the office."
The woman told Corriere that she was harassed over a period of time and quit the Italian football federation she said she had decided to come forward when she realised that Tavecchio's resignation did not signal that he intended to quit the sport.
On Monday, Tavecchio, who is 74, finally heeded calls to go following Italy's elimination in a World Cup playoff against Sweden a week earlier.
At a press conference to announce his decision, he said he regretted that he was the only person at the federation to have resigned.
Before becoming head of the federation, Tavecchio ran Italy's amateur football leagues.
"When I understood that Tavecchio's intention was to take another position of responsibility, perhaps with the amateurs, I had no doubt that it was time for me to speak up," Mary said.