No. The New Testament treats the Sabbath as a shadow that pointed to Christ, who is now our rest. You are free to set aside a day of rest, and it is wise, but you are not obligated to keep it for right standing, and no one should judge you over it.
The Grace Answer
Sincere believers worry they are sinning if they do not keep a strict Sabbath. The New Testament lifts that weight directly. The Sabbath was part of the old covenant law, and like the rest of that law, it pointed forward to Christ and finds its fulfillment in Him.
Paul says it plainly: let no one judge you in food or in drink, or regarding a festival or a new moon or sabbaths, which are a shadow of things to come, but the substance is of Christ. A shadow is cast by a coming reality. Once the reality arrives, you do not cling to the shadow. The Sabbath was the shadow. Christ is the substance. He is now your rest.
Rest as a Person, not a rule
Hebrews picks up the same theme: there remains therefore a rest for the people of God, and the one who has entered it has himself also ceased from his works. The deepest Sabbath was never mainly about a calendar. It was about ceasing from your own striving to earn God’s favor and resting in finished work. In Christ, you have entered that rest every day, not just one in seven.
This is the pattern with the whole old covenant law. Each part was a shadow, a preview cast ahead of time, and every shadow was thrown by the same body, Christ. The Passover lamb, the temple, the priesthood, the Sabbath, all of them pointed to Him. When you have the Person, you do not move back into His shadow. So are you required to keep a weekly Sabbath for right standing? No. Paul leaves it to freedom: one person esteems one day above another; another esteems every day alike. Let each be fully convinced in his own mind. If setting aside a day to rest and worship refreshes you, wonderful, and it is genuinely wise for body and soul. If someone insists you must, or judges you for how you keep it, they have turned a shadow back into a chain.
Enjoy rest as a gift, not a test. The point was never the day. The point was always the Person the day pointed to, and He is your rest now.