Islam is associated with the color green because of green's special properties.
Green falls in the middle of the visible spectrum. In the Qur'an, the Muslim community is described as the "midmost" nation:
"Thus, We appointed you a midmost nation that you might be witnesses to the people and that the Messenger might be a witness to you." (2:143)
The Arabic word for "midmost" is wasat. According to commentaries on the Qur'an, wasat implies being both just and balanced.
The middle avoids excess, neither elevating the prophets beyond their roles, nor falling short in praising and following them. Islam is "on the middle course and the path of moderation." (At-Tirmidhi)
Green also sits between yellow and blue in the visible spectrum. Symbolically, yellow represents the heavens and blue represents the earth. Humans are a blend of earthly and spiritual attributes--living in this temporary world with an eye toward the eternal abode. If you mix yellow and blue together, green results. Green is a mixture of heaven and earth.
The Prophet Muhammad, may Allaah bless him and grant him peace, said
"Be in the world as if you were a stranger or someone traversing a way." (Imam an-Nawawi, Hadith No. 40)
Islam teaches us not to become attached to this world but to work toward our ultimate destination.
Green also represents life. Leaves are green because of chlorophyll, which enables plants to make food from light. In the fall when chlorophyll molecules break up, plants no longer make food and they become dormant. Plants return to "life" in the spring when the green pigment returns.
So, if you look at the signs in nature, green represents moderation, internal balance, and life. No other color more perfectly describes Islam.
For more info: The Koran Interpreted, About Rainbows, Photosynthesis