The SFA said Strathclyde Police have issued the advice after their names were posted on fans' forums and social networking sites.
An SFA statement said the three had been subjected to "abusive and threatening communication" after their identities were "compromised."
The move came a day after Rangers manager Ally McCoist called for panel members to be named.
Earlier this week, Rangers were hit with a 12-month transfer embargo on players over 18, while owner Craig Whyte has been banned for life from involvement in Scottish football. The club, which is in administration, was also fined £160,000 after being found guilty of five rule breaches.
A spokesman for the SFA said: "We are deeply concerned that the safety and security of judicial panel members appointed to a recent tribunal has been compromised by a wholly irresponsible betrayal of confidential information.
"The judicial panel consists of volunteers from across the spectrum of sport and business. They are appointed on the basis of anonymity yet all three panel members have reported intrusion into their personal and work lives, including abusive and threatening communication.
"This has been extended to directors of the Scottish FA, whose private details have been published on internet sites and who have, themselves, been victims of abusive communication.
"This culminated in a visit by Strathclyde Police, who are taking seriously the threats made towards the individuals involved. We are thankful for their advice and support."
It has been reported that one of the individuals said he is now considering his future involvement in the process.
He told a sports website he could not discuss the case. But he said: "I hope that when the statement of reasons is published by the SFA, that responsible people will understand the reasons for the decision. I have no axe to grind with any football club."
Rangers fans reacted angrily to the sanctions imposed and supporters have organised a march to Hampden in Glasgow to protest against them.
Protest – Stop The SFA claims the sanctions "jeopardise the future of our club and of Scottish football". The organisers intend the march to leave from Queen's Park at 1.30pm on Saturday.
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