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.
OK, daze, but that isn't really helpful if I'm the DM
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.
