We've learned ... Sesame Workshop lawyers recently met with a 23-year-old man who claims he and Clash began a sexual relationship 7 years ago ... when he was 16 and Clash was 45.

Clash has acknowledged to TMZ he had a relationship with the young man -- but insists it only took place AFTER the accuser was an adult.

Sesame Workshop honchos tell TMZ ... "In June of this year, Sesame Workshop received a communication from a young man who alleged that he had a relationship with Kevin Clash beginning when he was 16-years-old. This was a personal relationship, unrelated to the workplace. We took the allegation very seriously and took immediate action."

Sesame Workshop officials acknowledge to TMZ they met with the accuser twice and had a number of other communications with him.

Sources with direct knowledge of the situation tell TMZ ... after the accuser's initial meeting with Sesame Street, the accuser felt Sesame Workshop's lawyers were trying to muzzle him ... so he lawyered up with Andreozzi and Associates -- the firm that represented one of the victims in the Jerry Sandusky child rape case.

On August 15, 2012 ... Andreozzi fired off a letter to Sesame, accusing the company of trying to "discredit the victim in order to protect its employee and the image of one of its most valuable characters," adding, "This approach places a greater value on a puppet than the well being of a young man."

Sesame Workshop officials tell TMZ ... they conducted a thorough investigation and determined the allegation of underage sex was unsubstantiated. They say they never tried to silence the accuser -- rather they asked for evidence supporting his claim, but he never produced it.

Officials also tell us they're suspicious because the accuser has an email which TMZ obtained -- purportedly sent to him by Clash, acknowledging they had the affair when he was 16. The officials say the accuser never mentioned such an email existed and they believe it's fraudulent.

But there were other emails between Clash and the accuser, and although they don't suggest there was underage sex, officials tell us they disciplined him for inappropriate use of company email.

Sesame Workshop honchos tell TMZ ... "Kevin insists that these allegations are false and defamatory and he has taken actions to protect his reputation. We have granted him a leave of absence to do so."

It is unclear why Clash wanted a leave of absence, since he denies the allegations of underage sex.

As for Clash, the voice actor tells TMZ, "I had a relationship with [the accuser]. It was between two consenting adults and I am deeply saddened that he is trying to make it into something it was not." Clash calls the accusations false and defamatory.