The meal with Gov. Chris Christie at Drumthwacket will celebrate the Muslim holy month.
Several of the invited Muslim leaders met recently with the state's attorney general, who announced in May that the New York Police Department had not violated any New Jersey laws in conducting surveillance at Muslim businesses, mosques and student groups in the state.
The attorney general's findings angered many Muslims, but several of those invited to Tuesday's dinner said Ramadan is not a time for politics.
Christie's spokesman, Michael Drewniak, did not respond to a request for comment on the Ramadan meal.