Because the modulation transfer function and point spread function are related by a Fourier transform their widths, as defined by variances, will obey a Heisenberg uncertainty principle type relation:
$$\sigma_{\mathrm{PSF}} \sigma_{\mathrm{MTF}} \ge \frac{1}{2},$$ where the lower bound is obtained for Gaussian functions.
If the width needed is not the standard deviation, but the functions are Gaussian, then it is possible to adapt the inequality. If the width is related to the standard deviation as $w = c \sigma$, for some numerical constant $c$, then the equality becomes:
$$w_{\mathrm{PSF}} w_{\mathrm{MTF}} \ge \frac{c^2}{2},$$ so you'll need to figure out the constant of proportionality that relates the desired width to the standard deviation.
The exact relationship for non-Gaussian functions will depend on the details of the functions in question. If what you have is an empirical curve, you'll probably want to feed it into a Fast Fourier Transform function to get an empirical curve for the matching function.