The player in question is scrum-half Tyson Keats, who appeared in 10 Premiership games this term while not holding effective registration with the RFU.
It follows a case heard by a Rugby Football Premiership regulations panel on Tuesday, with the verdict announced by the RFU on Thursday night. Welsh, who now go bottom of the Premiership two points behind Sale Sharks, had a further five-point deduction suspended until the end of next season.
The decision leaves London Welsh facing an uphill battle to avoid relegation in their first season of Premiership rugby. They have just five games left - away to Gloucester, Bath and London Irish, and at home against Northampton and Worcester - and are now favourites for the drop.
The case surrounding New Zealander Keats was visa-related, and Welsh now have 14 days in which to appeal the decision.
Their next Premiership fixture is at Gloucester on March 23.
Panel chairman Jeremy Summers said: "This was an extraordinary case, and one that it is hoped will never be repeated.
"The sanction imposed was structured to reflect the seriousness of the matter, which included conduct that was dealt with by the police, but also to import a rugby-based proportionality to the overall position that took into account the wider interests of the game."
Summers was joined on the panel by Premiership Rugby chief executive Mark McCafferty and Peter Budge. London Welsh's former rugby manager Mike Scott is the subject of a separate RFU disciplinary hearing relating to Keats' registration.
Scott has been charged under RFU rule 5.12 for 'conduct prejudicial to the interests of the Union or the Game'. Scott's case will be heard at a later date.