EPCR said it "does not condone the entry of a spectator to the field of play" and called it a "regrettable incident."
Munster head coach Johann van Graan was asked about the incident post-match but a spokesperson for the province stepped in to state that they would be making no comment on the issue.
Vunipola was warned by his club and the Rugby Football Union this week for defending Israel Folau's condemnation of gays.
"People say I put my foot in it so I have to deal with it," Vunipola said.
The number eight told BBC Radio 5 Live: "It's not something I'm afraid of. I probably have to expect that it's going to keep happening.
"It was quite a motivating factor that people were booing me. I wanted to back up my words and show my team-mates that I did not mean to distract them."
The fan who confronted Vunipola was quickly led away by stewards.
European Professional Club Rugby, the tournament organisers, said: "Following the regrettable incident at the Ricoh Arena, the spectator in question is currently being detained by the stadium authorities."
Last week Vunipola was criticised for 'liking' an Instagram post from Australia winger Folau which warned gay people that hell awaited them unless they repented.
Folau later had his contract cancelled by Rugby Australia.
Vunipola defended his views, writing on Instagram: "There just comes a point when you insult what I grew up believing in that you just say enough is enough. Man was made for woman to procreate, that was the goal no?"
Vunipola said after the game on Saturday: "It was probably insensitive, but also something I strongly believe in.
"I'll probably not be as honest as I have been about things that probably hurt a lot of people. I know that now.
"I'm not going to change the happy-go-lucky person I am. My faith is what got me to this position. It's something I'll stick by.
"It's been awesome having friends supporting me, whether they agree with me or not."
