The club were charged by the governing body of failing to ensure that its players and/or club officials conducted themselves in an orderly fashion following the final whistle of their side's controversial Championship match at Swansea City on March 6.
Boro denied the charge, but an independent regulatory commission found the charge proven during a subsequent hearing and have now imposed this sanction.
Boro lost the game 2-1 following a stoppage-time penalty from Andre Ayew on an afternoon when the visitors were livid at a number of decisions coming against them.
Furious manager Neil Warnock was subsequently handed an improper conduct charge after his comments to the media after the game.
The Boro boss was left frustrated by decisions made by referee Gavin Ward on the day as he missed a tackle on Anfernee Dijksteel that ended the defender's season, disallowed a perfectly good Boro goal and then awarded the Swans a late penalty despite initially pointing for a corner.
The veteran manager was subsequently fined £7,000.