The report published by the BBC states that complainants said it was “offensive to feature two men dancing as a pair”.
TV watchdog Ofcom also confirmed to HuffPost UK it had received one complaint, but their process is that people should complain to the BBC first.
However, the complaints are at odds with the positive response the routine received on social media.
Viewers hailed the dance, which was the first time the show had featured an individual same-sex routine, as “emotional”, “progressive” and claimed it made their hearts “burst”.
Graziano and Johannes were seen dancing as Emeli Sandé performed her recent single Shine, with Johannes later saying it had made him feel “so liberated”.
Speaking to Hello! magazine, he said: “For the first time in my life, I feel accepted for who I am. That says so much about the people of this country.
“To be able to dance with a friend I respect and adore is joyous. There’s bromance galore between us, but there were no male and female roles, just free movement.
“It was beautiful, classy and elegant.”
HuffPost UK has contacted the BBC for comment about the complaints.
Earlier this year it was reported that Strictly would be introducing a same-sex couple into the competition next year, which prompted a response from the BBC, confirming they’re now “completely open” to the idea.
A Strictly rep said: “Strictly Come Dancing is an inclusive show and we are proud to have featured same-sex dancing amongst the professional dancers in group numbers in previous series.
“We are completely open to the prospect of including same-sex pairings between our celebrities and professional dancers in the future, should the opportunity arise.”
Strictly Come Dancing continues on Saturday at 7pm on BBC One.