... vergl. mal mit Antwort #6 hier: Siehe auch: Kündigung zum Ende des Halbjahres - #6 . . .

I would say:

The employee's employment may be terminated upon one month's notice, effective as of the end of the month.

I occasionally see translations that say "to (X date)" as in the thread Daddy links to in No. 1, but I wouldn't accept that wording for AE.

Clearer yet: Termination takes effect at the end of the next calendar month after the date of this notice. "Effective as of the end of the month" is unclear as to what is effective (the notice or the termination itself) at the end of which month.

Thanks - I'll go with Katydid's suggestion, here's my reasoning: it is closest to the original (Kündigungsfrist has to be in there) and it is as clear - or unclear - as the German original, plus if the notice is effective as of the end of the month, so is the termination of the working contract.
Does that make sense?