It is not an exact rule. The minimax value is the solution to the optimization problem described by Donoho and Johnston (http://www.jstor.org/stable/2337118). Their description of the problem is quite convolved, but (for soft thresholding) they simplify it to: find the zero of the function:

$p(\lambda) = (1 + \lambda^2) * (2*(n + 1) * \Phi(-\lambda) - 1) - 2*\lambda * \phi(\lambda) * (n + 1)$

for \lambda between 0 and $\sqrt(2*log(n))$, being \Phi the normal cumulative probability function, and \phi the normal probability density function.

The rule you mention is contained in many papers, but as far as I have been able to track, all they refer to Matlab's algorithm. It seems to be a closed-form approximation to the optimal value.