"In this tongue-in-cheek ironic statement..." is the beginning of a sentence in my essay. Is "tongue-in-cheek ironic sentence" redundent?

no

I disagree. I think it is redundant.

http://en.wikipedia.org/wiki/Tongue-in-cheek

http://www.phrases.org.uk/meanings/tongue-in-cheek.html

Yes, the phrase "tongue-in-cheek ironic sentence" can be considered redundant because both "tongue-in-cheek" and "ironic" convey similar meanings. However, it's important to consider the context and tone of your essay before making any changes. If you believe that both terms are necessary for conveying your intended meaning, you can keep the phrase as it is.