Cockerill was found guilty of using words that were "obscene, inappropriate and unprofessional" by a Rugby Football Union disciplinary hearing convened on July 1.
The former England hooker's conduct was deemed to be prejudicial to the interests of the Union and/or the game contrary to RFU Rule 5.12.
The RFU announced this evening that the appeal is against the sanction only and will release details of a date and venue in due course.
The original charge related to the events at Twickenham on May 25 when Cockerill reacted angrily to a tackle by Courtney Lawes on Toby Flood and left his seat to discuss the incident with Terheege, who was on the touchline.
Cockerill pleaded not guilty to the charge but the RFU panel decided he had acted in an "inappropriate and unprofessional" manner and banned him until November 3.
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