The Colombian will miss three games after the Ibrox club opted not to challenge a Scottish Football Association notice of complaint for stamping on Hibernian defender Ryan Porteous.
Morelos will miss Scottish Premiership games against St Johnstone, Hamilton and Kilmarnock.
The charge carries a two-game ban but the 24-year-old will serve one further match because it is his second such offence this season. He was cited for a forearm smash on Dundee United defender Mark Connolly in December.
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Morelos scored the only goal of the game at Easter Road last week after referee Kevin Clancy saw nothing wrong with the incident.
However, the flashpoint was flagged in the SFA disciplinary procedures and three former grade-one officials decided it was worthy of a red card.
Rangers had until 3pm on Monday to decide whether to challenge the charge and a hearing pencilled in for Tuesday will now not go ahead.
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