Exactly the same issue here on a test system...
When clamscan is scheduled for weekly runs, the permissions for /bin/bash will be wrong on Monday morning.
I changed the schedule for the clamscan job to daily (after resetting the permissions) and the problem will be back every morning....
I do not blame clamscan, I suspect it might happen only on (old) slower systems where clamscan runs that long that it might interfere with another regular cron job???? Clamscan runs 1,5h on this old test server.
I manually changed the clamscan starting time from 0:00 to 2:00 to see whether there might be a specific other job running at that time but the result after 2:00 is as bad as at midnight. For the moment I have disabled the clamscan and all is fine....
Regards,
Michael