There are many forms of Arabic spoken in the Middle East, but
Arabic as a written language does not vary at all from society to
society: written Arabic is referred to as Classical Arabic and is
not commonly spoken. In fact there is no written language for
Arabic dialects, as they are only spoken and grammatically
incorrect, these dialects are part of the Modern Standard Arabic
languages.
Classical Arabic has been a literary language and the liturgical
language of Islam since its inception in the 7th century, and is no
longer evolving or progressing in terms of invention of words,
terminology or variation of grammar. The only reason Classical
Arabic is not a dead language is because there is no proper way of
writing the different Arabic dialects and because The Koran is
written in Classical Arabic.
So to answer your question: No, Arabic is not a modern
language.