Vunipola scored Saracens’ second try in an impressive 32-16 semi-final triumph.
A picture of the incident showed Vunipola being approached by a man wearing a Munster shirt, gesturing at him with his fingers as Vunipola joined team-mates on a lap of honour.
The number eight had been booed most times he touched the ball at Coventry’s Ricoh Arena, where Munster fans heavily outnumbered Saracens supporters among a 16,000 crowd.
Vunipola received formal warnings from his club and Rugby Football Union in the past week after he posted on social media that “man was made for woman to procreate that was the goal no?”
He also liked a social media post from controversial Australian star Israel Folau that stated “hell awaits” for homosexuals.
A few rainbow flags – symbol of the lesbian, gay, bisexual and transgender movements – were visible among the crowd in Coventry.
In a statement, European Professional Club Rugby said: “EPCR does not condone the entry of a spectator to the field of play.
“Following the regrettable incident at the Ricoh Arena, the spectator in question is currently being detained by the stadium authorities.”
Vunipola, meanwhile, said there was “no intention to hurt anyone” following his social media post and support for Folau.
He told BT Sport: “Behind closed doors, I felt a lot of love, a lot of kindness shown to me. I am just very grateful to be part of this team.
“From my point of view, I believe in what I believe in.
“There was no intention to hurt anyone. I am just grateful to play.”
Saracens rugby director Mark McCall said he did not see the post-match incident, while a question on the matter to Munster boss Johann Van Graan at his press conference was blocked by one of Munster’s media team.
McCall said: “Billy was outstanding today, and so were all of his team-mates, to be honest.
“As a group, we were determined not to let this week pass us by because we work incredibly hard to be involved in weeks like this one, games like this one.
“And we ended up having a brilliant week, and you can see that in the performance today. You could see how tight we were.
“The club dealt with it (Vunipola social media posts). It’s been dealt with, it was dealt with decisively, it was dealt with quickly and it was dealt with, in my opinion, fairly.
“Then we just got on with the rugby, and that’s what we are here to do, get on with the rugby.
“I thought we played really well. Although the scoreboard said 12-9 at half-time, it didn’t feel like that.
“The thing that pleased me most was that the players understood that the scoreboard did not necessarily reflect how well we had played and what we were building towards.
“I was just really pleased with our intensity, which was relentless the whole game, and the control we had emotionally as well.”
Despite wing Darren Sweetnam’s try, two Tyler Bleyendaal penalties, a long-range Conor Murray strike and JJ Hanrahan conversion, Munster suffered a seventh successive European semi-final defeat on their record 14th appearance in the competition’s penultimate knockout stage.
Van Graan added: “We came here to win, but we were beaten by a better side on the day.
“Sometimes you have just got to say well done to the opposition.
“They are unbeaten in this season’s tournament and have been playing some fantastic rugby, and you have got to concede that you weren’t as good as your opposition on the day.”
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