Speight was sent off last week for slamming Stormers centre Juan de Jongh head-first into the ground in his side's 39-19 playoffs victory in Cape Town and subsequently banned on Wednesday for five weeks for the incident.
Ruling body SANZAR, however, said on Friday they had received notice the Brumbies would appeal the ban.
The appeal hearing would take place on June 30.
The Brumbies play the Hurricanes in Wellington on Saturday in the first of Super Rugby's semi-finals, though a SANZAR spokesman said that Speight would not be able to play as the initial ruling was still in force.
Original source: Brumbies appeal Speight ban