Democratic Party politicians had accused Noppadon of supporting Cambodia in a row over the cliff top Preah Vihear temple that both countries claim as their own.
"I insist that I have done nothing wrong. I have not sold out the country"
Unesco, the United Nations' cultural organisation, granted World Heritage status to the temple on Tuesday.
On the same day however Thailand's constitutional court ruled that Noppadon acted unconstitutionally when he endorsed Cambodia's Unesco application without first consulting the Thai parliament on the matter.
Announcing his resignation on Thursday an emotional Noppadon said he was quitting to "take responsibility so that the country can move forward".
"I insist that I have done nothing wrong. I have not sold out the country. I love Thailand, and would not cause any damage to the country."
Ctitics said the endorsement undermined Thailand's own claim to land near the temple.