The man, who called himself "Dave from Chelsea media", left a recorded message saying that the figures published by the donor information website on Premiership teams' giving to charity in March "undermined everything that Chelsea Football Club does in its work in the charity sector".
A Chelsea spokesman denied that the man had any link with the club. "He is not a representative of Chelsea," he said. "Clearly we do not advocate any kind of physical violence."
In the message, available today on the Intelligent Giving site, the caller said its staff should "get a proper job" before saying: "I'm going to punch you in the face."
'Dave' is included in the site's list of 'People who don't like us', alongside Megan Pacey of the Institute of Fundraising. She said: "Their practice is improving."
- Listen to the telephone message here