Experts and BHG readers answer.
A "cool" fire, from just leaves and weeds and such, should not harm the grass. It's only March, and grass in your region should not have begun to grow, so no worries that you haven't yet seen green growth.
You don't say what sort of grass you have, and in Missouri, it could be any number of types. But zoysia may not green up until May. Bluegrass and Fescue should get rolling sometime in March, depending on if you're in North or South Missouri.
It's possible, if the fire was hot enough (if a pile of wood burned, for example) that the grass in that spot was killed. In that case, just scratch in some compost, and replant. You won't know until spring green-up whether any areas have been killed, but it's no big hurry. Just see what grows this spring, and replant the areas that don't.
In the meantime, rake up any large debris (branches, leaves, and the like) but leave the ashes and smaller, loose debris (like decomposed leaves).