Rabeni was suspended when he appeared before a three-man RFU panel earlier this week, sidelining him until early July.
He had been cited following a Guinness Premiership game against Saracens at Welford Road last month.
He was found guilty of illegally making contact with the eye of an opponent, although Rabeni claimed contact with Saracens hooker Andy Kyriacou was accidental.
Leicester have now started the appeal process.
"Our legal team are now drafting a notice of appeal which will be filed to the RFU's disciplinary officer later today," said Tigers' head of rugby operations Simon Cohen.
"He will then set a time and date for the appeal to be heard."