Killie defender Tim Clancy has also been hit with the same punishment by the Scottish Football Association's disciplinary committee following a separate incident in the same match.
Rasmussen will miss the SPL visit to Dundee United on Sunday, April 25, although he has the right of appeal.
Rasmussen lashed out at Wright as the Kilmarnock defender held him in the home side's penalty area during Celtic's 3-0 quarter-final win.
The Dane was the victim of Clancy's indiscretion when the Irish defender stamped on him.
Clancy did not attend the meeting so his ban will come into effect seven days after the decision is confirmed in writing, but he is set to miss Killie's crucial clash against relegation rivals St Mirren in Paisley on April 24. The 25-year-old also has the right of appeal.
Both players will also have 12 points added to their disciplinary total after they were found guilty of "misconduct of a significantly serious nature".