Translation:Mother's day will be next month.
"Mother's day will be next month." -- this sounds like you are deciding which month mother's day will be (rather than saying that mother's day is next month). By my understanding this isn't the same meaning as the Russian sentence, but correct me if I'm wrong.
Absolutely right. In English we say, "Mother's Day (or any other event) IS next month". My guess is that this is the norm for impending (as in next week, month, semester) events, because when speaking of events further out, we would use the explicit future, e.g. "Christmas will be on a Tuesday next year."
Native Russian speaker here: this is a perfectly normal sentence for both of the meanings. If nitpicking, you could leave off 'будет' and it would be a little bit better for implying what you are talking about, but the difference is almost nonexistent - it would still have both meanings
To all wondering about the apostrophe: It actually is Mother's day. The meaning is that everybody is celebrating their own mother - not mothers in general. This is the founder's explanation and she insisted very strictly that the apostrophe goes before "s".
In Russia международный женский день (International Women's Day) is being celebrated. It even is an official holiday.