Hibernian stalwart Stevenson was accused of attempting to stamp at Walker as he shielded the ball near the touchline in an attempt to run down the clock. Reacting angrily to that challenge, Hearts winger Walker appeared to aim a head-butt at Stevenson.
Having reviewed the video evidence, Scottish Football Association compliance officer Vincent Lunny - enduring a busy final month in the position as he prepares to hand over to Glasgow lawyer Tony McGlennan - charged both men for their part in the incident, offering them two-game suspensions.
Hearts moved quickly to agree to the ban, with a spokesperson confirming: "The club has accepted the offer of a two game ban and will not be appealing."
Walker will now miss tonight's Petrofac Training Cup tie against Livingston and their SPFL Championship encounter at Raith Rovers this weekend. Their capital city rivals also accepted the ban: "Hibernian can confirm the club will not be contesting against the notice of complaint issued against Lewis Stevenson following Sunday's Edinburgh derby at Tynecastle."
Stevenson will sit out the upcoming matches against Falkirk and Dumbarton.
Speaking prior to the notice of complaint, Walker's teammate Gary Oliver insisted it would be "harsh" to punish the Hearts man - given the provocation of Stevenson's challenge seconds earlier.
"It would obviously be a bit harsh on Jamie, but it's not my job to concentrate on that," said Oliver. "We need to put the derby behind us and focus on Livingston."
Following the fiery affair, which Hearts won 2-1 thanks to goals from Sam Nicholson and a Prince Buben penalty, Hibs manager Alan Stubbs said: "I think the lad [Walker] has put his head on one of our players at the end, so it will be interesting to see what happens with that.
"Before the elbow incident, there were a couple of other flying elbows."