A very difficult situation but as previous commenters have said if this has only come to light on board then the Captain has been left with no option but to do what he did. To just have a quiet word in her ear to say she's ill when the entire rest of the crew and god forbid pax know what's actually going on would have destroyed his credibility entirely. We don't know for a fact he's radioed ahead for police. He's perhaps radioed ahead explaining the situation to OPS who have taken action.
The fact of the matter is this is probably a high-functioning alcoholic who will now hopefully get the help she needs. The stigma around mental health and addiction is well above average in the aviation industry and seeking help has probably not been an option for this person for fear of losing her income. Shame.
Edited to add she may well have been drinking throughout the duty so noticing in the briefing may not have been possible. He may even have been alerted to this by another member of the cabin crew.