Methylene blue is actually used to treat acquired cases of a similar condition called methemeglobinemia which is when the iron in heme is oxide from Fe2+ to Fe3+ [1]. This is different from carbon monoxide poisoning which is caused by carbon monoxide binding more tightly to hemoglobin than oxygen preventing oxygen from effectively getting into your blood.
[1] https://www.uptodate.com/contents/methemoglobinemia?search=m...