Edit: After half day, my wife’s Mac started having the same problem. I have then applied the solution that I found in the Apple
iMessage Outage Affecting 30% Of Users
A couple of you have been in touch to let us know about an iMessage outage and now it has been confirmed by Apple that iMessage suffered an outage earlier today for around 30 minutes which affected around 30% of users around the world.
It still appears that iMessage is down for some but hopefully it will be returning to normal very soon.