The Three Lions coach, on behalf of the Football Association and at the request of FIFA, has issued an email to ticket holders asking them to refrain from offensive chanting
The teams have not played each other since 1995, when rioting England fans forced the fixture at Lansdowne Road to be abandoned after just 27 minutes.
And now Hodgson has urged Three Lions supporters to refrain from deliberately provocative "religious or political" chants aimed at the travelling team.
"England fans are rightly renowned for their passionate backing of the Three Lions wherever and whenever the team plays, at home or abroad," Hodgson writes in an email which fans and ticket holders will receive on Tuesday.
"With this next match coming in the middle of half-term week, it promises to be a great family occasion and everyone in the stadium should be able to enjoy it.
"Ahead of the Ireland fixture, on behalf of the FA, I would like to ask our supporters to please respect our opponents and welcome them in the right way.
"Wembley is considered the world over as the home of football and we ask those attending to not take part in any chanting - particularly of a religious or political perspective - which could cause offence to our visitors or fellow fans."