Yes, all spoken languages have both consonants and vowels.
But If you are talking about writing, the Hebrew alphabet only has consonants.
In the 10th Century, a system of markings below the words (called nekudot) indicate vowel sounds. Often the vowels are left out in print, but the words can be understood from their contexts.
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If you are talking about the writing system of Hebrew, it has 22 consonants. If you are talking about the phonology of Hebrew, modern standard Hebrew (not the yemini dialect) has 19 consonant sounds plus 4 foreign consonant sounds used in borrowed words.
The Yemini dialect in Israel adds 2 additional consonant sounds, but this is an endangered dialect.