Uefa says it “strongly condemns” the abuse received by Premier League referee Michael Oliver and wife Lucy.
BBC Sport understands Lucy Oliver – a Women’s Super League referee who also officiates men’s non-league football – received threatening texts after her mobile number was posted on social media following the game.
“Uefa strongly condemns the abuse directed at Michael Oliver and his wife,” said European football’s governing body in a statement to BBC Sport.
“We have been in contact with them to offer our support and we trust the relevant authorities to take action against those individuals who have behaved inappropriately both on and off social media.”
In a dramatic end to the match at the Bernabeu in Madrid on Wednesday, Juventus captain Buffon was sent off for confronting Oliver over the 93rd-minute penalty decision.
Buffon later told media the English official had a “bag of rubbish for a heart” and defended his comments on Saturday, saying he “stands by all of it”.
Following the match, Lucy Oliver’s Twitter account was targeted by some supporters posting abusive messages.
“We are aware of threatening messages being posted on social media,” a Northumbria police spokesperson told BBC Sport.
“This type of behaviour is completely unacceptable and those writing the messages need to be aware that they could be committing a criminal offence.
“Neighbourhood officers are in touch with the victims in this case to offer them support and ensure any further offences are reported to police.”
A spokesperson for Twitter confirmed that several offensive tweets reported by Lucy Oliver have been removed for violating its abuse policy.
Ref Support chief exec Martin Cassidy said his organisation has also been in touch with Lucy Oliver to offer its support.
“I know other people are supporting her, she’s always been a dynamic educator and a good referee,” he said.
“It seems more and more acceptable in terms of the abuse of officials. It seems fair game but it has to stop.”
Juventus manager Massimiliano Allegri also said he “understood” Buffon’s reaction and described him as a “role model on and off the pitch” for the “last 20 years”.
Oliver was the fourth official for Huddersfield’s late win over Watford in the Premier League on Saturday and is due to take charge of West Ham v Stoke City on Monday night.
In response to the online abuse of Lucy Oliver, some Italian football fans started a twitter hashtag #ItaliaLovesMichaelOliver backing the official, which got 6,000 tweets in 24 hours on Thursday.