Close-minded was first, but closed-minded is dominant:
Here's the earliest close-minded reference I can find from a Narrative of a Journey in the Interior of China, by Clarke Abel, 1818:
I found closed minded back to 1913 in The Century Magazine:
Edit:
After considering @FumbleFingers' comments here and his subsequent answer, I have to agree that most of the earlier close-minded references found through Google Books (including the one above) are using close |kloʊs| in this sense (from NOAD):
• not willing to give away money or information; secretive : you're very close about your work, aren't you?
This is also proven by this definition of uncommunicative from John Craig's A New Universal Etymological Technological, and Pronouncing Dictionary of the English Language, 1859:
It seems the phrase was once a common description for someone who "kept their own counsel"—usually used as a derogative, but sometimes as a compliment.
However, I did find this earlier use of close-minded specifically to mean the opposite of open-minded from an 1898 issue of The Outlook:
I also found evidence of a shift towards this sense of close-minded in other writings by the early 1900s. So, to conclude, I think the only thing new about the confusion evident by the 1960s was the frequency of the two terms in print.
I realize this may not ultimately answer the question, which is correct, but the timeline seems significant to me.
Best Answer
Consider:
Or, more formally: