The England and Wales Cricket Board confirmed that Swann had been found guilty of a level-two breach, but escaped a ban.
Swann remained at the crease, and lifted his hands above his head, after he was given out lbw in Nottinghamshire's second innings as the last man, which allowed Durham the time they needed to secure victory.
"During Nottinghamshire's LV= County Championship match against Durham on 29 April-2 May 2013, Swann was reported by umpires Steve Garratt and Peter Willey for a level-two breach of the code (showing serious dissent at an umpire's decision by word or action)," an ECB statement read.
"The penalty for this offence is three penalty points which will remain on his record for a period of two years. The accumulation of nine or more penalty points in any two-year period will result in an automatic suspension."
Swann made his return from elbow surgery in the Trent Bridge match, taking four for 56 in the second innings as Durham chased down a victory target of 183 in 20.2 overs.