Adam Cox, 27, failed to appear at City of London Magistrates Court for his hearing but was convicted in his absence of "throwing a missile on to a football playing area".
It was unclear whether the pie was aimed at a particular player or whether it struck anyone.
In a written statement, Stamford Bridge steward Dominic Agbo informed London Magistrates' Court that he "saw the Bournemouth fan throw something (on to the pitch) between the corner flag and the goal."
The court also heard that Cox had served a three-year football banning order, applied in 2012, for a similar matter.
A warrant was issued for Cox, of Christchurch, Dorset, regarding the imposition of a new football banning order.
The match in question finished with a 1-0 Chelsea victory, after Eden Hazard scored an 86th-minute winner.
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