An answerer at Quora claims:

Colour vision is a result of cone cells. People with normal vision have 3 cone cell types: red, green blue. Of the 6-7million you have, 45% are green. Therefore, your eyes need to work less to perceive colour. Dark greens (pine tree green) are one of the most relaxing colours.

Answerers at AnswerBag have similar claims:

Green has great healing power. It is the most restful color for the human eye; it can improve vision.

Green is very restful to the eye and it's at the opposite end of the spectrum to red, which is also the most emotionally charged colour. So looking at green not gives your eyes a break, it calms you emotoinally.

None of these provide verifiable evidence.

This is distinct from the claim that looking outside might be good exercise for your eye muscles.

Does looking at the colour green relax your eyes more than other colours.