I suspect you'd somehow not rejoined the chain completely. I had a quicklink fail this morning after removing that chain for waxxing. Likely I hadn't clicked both sides home completely.
In the past I've had lower-speed chains where pin pushing and reinserting is the accepted way to open and close a chain. It is possible for a side plate to be poorly retained, because a pin is pushed too far in or not far enough. This is unlikely to be the cause, because your chain is 10 speed which is too thin for pin reuse. Instead you have to use a new "replaceable pin" every time, or use a quick-link, which look something like this:
You say it broke away from a master link - so the other option is a weakness in the chain. If it was new, could have been a manufacturing tolerance. If the chain was used it could have suffered damage in an accident or derailleur crash.
I had a chain once which got munched in the front disk brake (yes, really) and there was a 30 degree rotation in the chain for about 15 links. It was impossible to see normally, but gave strange clanking only under load, and occasional poor shifting.