If it's achilles tendon injury,generally speaking you need to take a rest from the activity that caused the injury. That can be from as little as one week to as much as months depending on the grade of the injury.
Relative rest is the treatment not total rest. During the relative rest period you can undertake activities that are easy on the tendons. Moderate cycling is one of these activities as is swimming.
Fortunately you are married to a physio so I don't need to go into the stretching exercises etc. that you need to do.
I hope the injury is not severe and that you make a quick and full recovery.