The answer to this question depends on a large number of factors. The divorce process usually includes a Court Order not only formalizing your divorce, but also making specific provisions for the custody and access to any children you and your former spouse had together. The provisions of that Order will set out the rights that each parent has, to be involved in the child’s life.
If you are the custodial parent, the Order may already incorporate terms that specifically limit your right to move with the child. If it does not, and you need to move for work, for family-related reasons (for example to care for an elderly parent), or to pursue an established romantic relationship, then you may be allowed to move even over the objections of the other parent — but generally the consent of the Court will be required.
In making its decision, the court will look at many factors, including the reason for the move, the limitations it may put on the other parent’s rights, and the impact (positive and negative) on the child’s relationship with extended family members. In short, the court will look at the child’s best interests in making the decision whether to permit the relocation.