We know that only God should be worshiped (see Exodus 34:14 and Revelation 22:9). Only God deserves worship. The question of whether we should worship the Holy Spirit is answered simply by determining whether the Spirit is God. If the Holy Spirit is God, then He can and should be worshiped.
Scripture presents the Holy Spirit as not merely a “force” but as a Person. The Spirit is referred to in personal terms (John 15:26; 16:7–8, 13–14). He speaks (1 Timothy 4:1), He loves (Romans 15:30), He chooses (Acts 13:2), He teaches (John 14:26), and He guides (Acts 16:7). He can be lied to (Acts 5:3–4) and grieved (Ephesians 4:30).
The Holy Spirit possesses the nature of deity—He shares the attributes of God. He is eternal (Hebrews 9:14). He is omnipresent (Psalm 139:7–10) and omniscient (1 Corinthians 2:10–11). He was involved in the creation of the world (Genesis 1:2). The Holy Spirit enjoys intimate association with both the Father and the Son (Matthew 28:19; John 14:16). When we compare Exodus 16:7 with Hebrews 3:7–9, we see that the Holy Spirit and Yahweh are the same (see also Isaiah 6:8 as compared to Acts 28:25).
Since the Holy Spirit is God, and God is “worthy of praise” (Psalm 18:3), then the Spirit is worthy of worship. Jesus, the Son of God, received worship (Matthew 28:9), so it stands to reason that the Spirit of God would also receive worship. Philippians 3:3 tells us that believers “worship by the Spirit of God and glory in Christ Jesus.” There is one God who eternally exists in three Persons. When we worship God, we naturally worship all three members of the Godhead.
How do we worship the Holy Spirit? The same way we worship the Father and the Son. Christian worship is spiritual, flowing from the inward workings of the Holy Spirit to which we respond by offering our lives to Him (Romans 12:1). We worship the Spirit by obedience to His commands. Referring to Christ, the apostle John explains that “those who obey his commands live in him, and he in them. And this is how we know that he lives in us: We know it by the Spirit he gave us” (1 John 3:24). We see here the link between obeying Christ and the Holy Spirit who dwells within us, convicting us of our need to worship by obedience and empowering us to worship.