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Currently there is no way to mute the mic on the camera, although I am sure this is something they will remedy in the future by making the Camera become a "device" much like the DualShock 4 and Headphones are today.
There are a few options today,
1) Unplug the camera when not using it. (Terrible work around)
2) Create a party chat where you are the only member while playing games.
3) Most games have a mute function so that you can Mute all players. This also mutes your microphone.
In the future, you will be able to hold the PS button, go to devices, select camera, and hit mute microphone.
Sony knows this is an issue, but unfortunetly there isnt enough time in a day to resolve all the current issues with the firmware overnight.