Strictly speaking, the answer is “No.” A person can be saved who has not been baptized.  However, the Bible makes it clear that baptism is extremely important and that those who have accepted Jesus Christ as their Savior and who have decided to follow Him, will be baptized. Let’s see what the Bible actually says about this matter.
Mark says, “He who believes and is baptized will be saved” (Mark 16:16, NKJV). Jesus told Nicodemus, “Most assuredly, I say to you, unless one is born of water [baptized] and the Spirit, he cannot enter the kingdom of God” (John 3:5, NKJV). Jesus further told His disciples to go everywhere preaching the gospel and making disciples and baptizing them in the name of the Father, Son, and Holy Spirit (see Matthew 28:18-20). If we read just these verses in isolation, we might think that it is impossible to be saved without being baptized. However, the Bible is clear that there is no saving virtue or merit in the act of baptism itself. Jesus is our only Savior (see John 3:16; Acts 4:12; 2 Corinthians 3:11; 2 Corinthians 5:17-21).
So baptism is not necessary for salvation in the sense that only Jesus can save us. He is our only Savior. And the act of baptism, itself, does not save us. But this does not mean that baptism is not important. It does not mean that we can be baptized or not as we choose—once we have believed on Jesus and accepted Him as our Savior. Jesus said, “If you love Me, keep My commandments” (John 14:15, NKJV). And He has commanded us to be baptized (see Matthew 28:18-20). A person who loves Jesus and accepts Him as his or her Savior, will want to follow Him in baptism.
Baptism is important, because it is a public declaration that we have accepted Jesus and are turning our back on the old life of sin and are now trusting Jesus to live a new life as a Christian. When we are placed under the water and raised back out of it, we are symbolically stating that we have died to sin, that our old life of sin has been buried, and that we have been raised to new life in Jesus—just as He died for our sins, was buried, and was raised to life again (see Romans 6:3-5).
There are a number of similarities between baptism and marriage. When a couple decides to get married, is the wedding ceremony ritual really necessary for a boyfriend and girlfriend to act like a husband and wife? No, the couple are still the same people before the wedding day. Yet, still worldwide everyone wants to have a wedding ceremony to publically announce that they are now married. The relationship of the couple is not based on the wedding, but it sure means a lot to the husband and wife. Baptism is like getting married to Jesus. It is the outward symbol of an inward change. Baptism may not be required to save you, but it sure means a lot to Jesus.
Just as marriage is the formation of a new family, so baptism is the entrance into the Christian family. In marriage one takes the name of one’s partner, and in baptism we take the name of Christ (Christian). God designs that marriage is to be an experience in which the husband’s and wife’s personal relationship is ever growing and improving throughout a lifetime. And He designs baptism to be an experience in which our personal relationship with Him grows and improves throughout our lifetime.
So, is baptism necessary for salvation? Strictly speaking, No. Because salvation comes only through the shed blood of Jesus on Calvary (see Romans 3:25; 5:9; Ephesians 1:7; Colossians 1:20; Hebrews 9:22; Revelation 1:5; etc.). However, those whom Jesus Christ has saved will gladly follow Him in the extremely important step of baptism.