By RAW, being charmed does not end concentration; it isn't listed in the things-that-break-concentration in PHB 203. 

However, it would still be up to the DM, if he so rules, that a check would be needed, as PHB 204 states: 

> The DM might also decide that certain environmental phenomena, such as a wave crashing over you while you’re on a storm-tossed ship, require you to succeed on a DC 10 Constitution saving throw to maintain concentration on a spell. 

Being _charmed_ isn't an *environmental* effect, per se, but in keeping with 5e's spirit of rulings-over-rules, I think leaving it up to the DM would be how it was intended. 

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OK, but that isn't really helpful if I'm the DM
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Consider the spell being concentrated on and the charmer in question. If the spell is detrimental to the charmer, a _charmed_ person would likely end the spell as  

> You can end concentration at any time (no action required). (PHB 203)

because, according to the rules on being _charmed_ in PHB 290: 

> A charmed creature can't attack the charmer or target the charmer with harmful abilities or magical effects 

Anything other than that, a check or ending concentration outright would be totally within the rules.