The following stochastic differential equation on \(\mathbb{R}^d\): \[ X^i_t=x_0^i+\sum^m_{j=1}\int^t_0\sigma^{ij}(X_s)d B^j_s+\int^t_0 b^j(X_s)ds,\quad t\in[0,T],\quad i=1,\dots,d,\tag{1} \] where \(x_0\in\mathbb{R}^d\) is the initial value of the process \(X\) and \(B= \{B_t,t\geq 0\}\) is an \(m\)-dimensional fractional Brownian motion of Hurst parameter \(H\in(\tfrac 12,1)\), is considered. The authors study the regularity of the solution to equation (1) in the sense of Malliavin calculus. They prove the differentiability of the solution in the directions of the Cameron-Martin space and the absolute continuity with respect to the Lebesgue measure of the solution under ellipticity condition on the coefficient \(\sigma\).