God rested not because he was tired, but because he had "completed His work" (Genesis 2:2). God, who is infinite in power, scope, knowledge, etc., does not need to rest from fatigue. Being tired is a function of biological organisms, and God is not a biological organism. God is described in the Bible as being spirit (John 4:24), and spirit does not have flesh and bones (Luke 24:39). Therefore, God is not biologically-based. Furthermore, God is eternal in both the past and the future (Psalm 90:2), and he is the only God (Isaiah 43:10; 44:6, 8; 45:5). This means that God is eternally existent in a self-sufficient manner. This further means that God does not need any outside energy source to complete him or replenish him because he's completely self-sufficient. Therefore, God getting tired makes no sense.
"And by the seventh day God completed His work which He had done; and He rested on the seventh day from all His work which He had done," (Gen. 2:2).
Also, the seventh day of God's rest has not yet ended. In the previous six days, each has a morning and evening, but the seventh day does not. Therefore, the seventh day is, so to speak, ongoing and God has been quite busy in the world.
Finally, God's rest on the seventh day is typological in the rest we have in Christ (Matthew 11:28). On the seventh day, which is the Sabbath day, the day of rest, Christians cease from their work, just as God did. But where we need to be replenished, God does not.