Electric field around a plane sheet is given by s/e where 's' is surface charge density and 'e' is permitivity of medium . This implies that electric field is uniform around a plane sheet that is no variation even with diatance . So my question is how long this will be present will it spread till infinity.

An electric field has no boundary unless it is blocked by something.

Kiwiheretic was correct in his first response.
Everything else said is consistent with this.
I have given you the conditions where your original statement is correct.

That is the field is only constant out to infinity for an infinite sheet.