I would recommend being explicit about this expectation with him. Some shy people are badly calibrated and have the erroneous impression that they are speaking too much already leading to their low contribution rate. Make him aware of this issue and get his response to why it is happening and working together to address whatever the issue is.
You may also want to directly call on him in meetings to solicit his opinion thereby forcing him to speak ("Hey Bob, we haven't heard your thoughts yet, what do you think about option XYZ?"). If you do this often enough, he may see that his fears about speaking up are unfounded.
You may also want to directly call on him in meetings to solicit his opinion thereby forcing him to speak ("Hey Bob, we haven't heard your thoughts yet, what do you think about option XYZ?"). If you do this often enough, he may see that his fears about speaking up are unfounded.