In this case, you can say It's a national holiday in the USA next Monday. or Next Monday is a US holiday. You need to use "a" in the second sentence because the "U" in "US" is pronounced like "you".

It's a holiday in the US.

The words in your question are even better. (Next) Monday is a national holiday. (If you are in the US) (Next) Monday is a national holiday in the US. (If you aren’t) Next isn’t necessary either.

Not "an" with "US", nor with "United States". It's a US holiday. - ok It's a holiday in the US. - ok