The Sabbath is something that we find as early as the second chapter of Genesis in the Bible.
1 Thus the heavens and the earth, and all the host of them, were finished. 2 And on the seventh day God ended His work which He had done, and He rested on the seventh day from all His work which He had done. 3 Then God blessed the seventh day and sanctified it, because in it He rested from all His work which God had created and made.
Even so, there is no a commandment given to observe the Sabbath until God gave the Law to Moses who brought it to the Israelites. This is found in both Exodus and Deuteronomy.
Exodus 20
8 “ Remember the Sabbath day, to keep it holy. 9 Six days you shall labor and do all your work, 10 but the seventh day is the Sabbath of the LORD your God. In it you shall do no work: you, nor your son, nor your daughter, nor your male servant, nor your female servant, nor your cattle, nor your stranger who is within your gates. 11 For in six days the LORD made the heavens and the earth, the sea, and all that is in them, and rested the seventh day. Therefore the LORD blessed the Sabbath day and hallowed it.
Deuteronomy 5
12 ‘ Observe the Sabbath day, to keep it holy, as the LORD your God commanded you. 13 Six days you shall labor and do all your work, 14 but the seventh day is the Sabbath of the LORD your God. In it you shall do no work: you, nor your son, nor your daughter, nor your male servant, nor your female servant, nor your ox, nor your donkey, nor any of your cattle, nor your stranger who is within your gates, that your male servant and your female servant may rest as well as you. 15 And remember that you were a slave in the land of Egypt, and the LORD your God brought you out from there by a mighty hand and by an outstretched arm; therefore the LORD your God commanded you to keep the Sabbath day.
This commandment was part of what is the decalogue, or what Christians refer to as the 10 commandments today. Most Christians will agree that these 10 should be kept regardless of New and Old covenant relations, and nearly all of the 10 are mentioned at some point in the New Testament in regards of observing them. Particularly for the Sabbath Law, there tends to be disagreement on what it means to observe the Sabbath.
If we look in the New Testament, there is Scripture that deals with this.
Hebrews chapter 4 speaks of the Sabbath rest, and how those it was first preached too didn't fully enter in the rest because of disobedience. It then says
9 There remains therefore a rest for the people of God. 10 For he who has entered His rest has himself also ceased from his works as God did from His.
Collosians 2:16-17 also says
16 So let no one judge you in food or in drink, or regarding a festival or a new moon or sabbaths, 17 which are a shadow of things to come, but the substance is of Christ.
It seems to be pretty clear that these things that were in the Law and dealt with the physical, such as regulations for food and for keeping certain days, were but a shadow of Christ. Christ fulfilled the need to keep these things in the physical, and allowed us to take on His righteousness in him so we would not have to try and keep them ourselves.