Leicester Tigers will hand lifetime bans to anyone found to have subjected players and their families to "vile and disgusting abuse" on social media.
The club said it was aware of "malicious content" posted after Saturday's 52-20 defeat by Exeter.
Leicester have contacted police and "reported this as a crime".
"The club is in no way above criticism - everybody at the club accepts that we are not where want to be," said Tigers head of brand Chris Rose.
"Every person at the club finds it an honour to work at Welford Road and so accept all opinions on how we are doing our jobs for our supporters, but when this tips over into foul abuse, the club will do everything in its power to make sure people that believe that is acceptable behaviour are found and dealt with.
"There is no place in society or the Tigers family for this, let alone in our sport which prides itself on the family-friendly nature of the game.
"We encourage any supporters that have any information that could be relevant to contact the club or Leicestershire Police and help us make a stand against anyone having to receive these kind of messages."
Captain Tom Youngs, who has been banned for three weeks after being sent off in the loss at Welford Road, was one of "several players to have family members targeted in posts".
"At the moment, we have not been good enough and accept that it means a lot to our supporters, who are entitled to have their say on our performances," said Youngs.
"However, no family members are deserving of being pulled in to that criticism and nothing of the sort myself and players have received in recent weeks is appropriate, ever."