A change-point estimation problem is considered for the data \(y_t=\mu_1+\eta_t\), \(t=1,\dots,[T\tau_0]\), \(y_t=\mu_2+\eta_t\), \(t=[T\tau_0]+1,\dots,T\), where \(0\leq\tau_0\leq 1\) is the change point, \(\mu_i\) are real numbers and \(\eta_t\) is a fractionally integrated process with fractionally differencing parameter \(d\), \(-0.5<d<0.5\), i.e. \((1-B)^d\eta_t=v_t\), where \(B\) is the back-shift operator and \(v_t\) is some ARMA process. The authors consider the case when \[ T\sum_{t=1}^{[T\tau]}\eta_t\Rightarrow \kappa B_d(t), \] where \(B_d(t)\) is a fractional Brownian motion. The least squares estimator \(\hat\tau_T\) for \(\tau_0\) is considered. It is proved that if \(\tau_0\in[\tau_L,\tau_R]\), then \[ | \hat\tau_T-\tau_0| =O_p(1/T^{0.5-d}(\mu_2-\mu_1)^2). \] If the change-point is absent, then \(\hat\tau\to\text{arg max}_{\tau\in[\tau_L,\tau_R]}\Psi_d(\tau)\), where \[ \psi_d(\tau)=\kappa^2 B_d(\tau)^2/\tau+\kappa^2[B_d(1)-B_d(\tau)]^2/(1-\tau). \] Results of simulations are presented.