My supervisor/project coordinator is going to get married soon and she has passed me the invitation. However I don't like weddings and I don't think we are close enough to attend such social organisation. Is there any way to handle this?
How would you politely turn down the invitation if they weren't a colleague?
There is no difference between this situation and receiving an unwanted invitation from another source. Depending on your culture, an acceptable response could be a grateful written reply, apologising for not being able to attend. Treat the invitation as a personal matter rather than a professional one, and if possible direct your response privately rather than via the workplace.
Personally when I was in a similar situation I sent the couple a card and a gift. I thanked the person who invited me and told them I wasn't able to attend because of other commitments.
If you aren't that close to your boss I doubt very much she will feel slighted if you don't attend. How many other people in the office have also received such an invitation? When I got married my wife gave an evening invitation to everyone in her office, we weren't offended that not everyone came.