Moral appraisals are found to be associated with a person’s individual differences (e.g., political ideology), and the effects of individual differences on language use have been studied within the framework of the Moral Foundations Theory (MFT). However, the relationship between one’s moral concern and the use of language involving morality on social media is not self-evident. The present exploratory study investigated that relationship using the MFT. Participants’ tweets and self-reported responses to the questionnaire were collected to measure the degree of their appraisals according to the five foundations of the MFT. The Japanese version of the Moral Foundations Dictionary (J-MFD) was used to quantify the number of words in tweets relevant to the MFT’s five moral foundations. The results showed that endorsement of the Fairness and Authority foundations predicted the word frequency in the J-MFD across all five foundations. The findings suggest that the trade-off relationship between the Fairness and Authority foundations plays a key role in online language communication. The implications and future directions to scrutinize that foundation are discussed.