The grass or turf of a playing field can greatly affect gameplay, as grass affects the spin of the ball, traction / drag, among other things.
In FIFA's Laws of the Game booklet, there is little specified about natural playing surfaces. The blurb only applies to artificial turf:
The colour of artificial surfaces must be green.
... the [artificial] surface must meet the requirements of the FIFA Quality Concept for Football Turf or the International Artificial Turf Standard, unless special dispensation is given by FIFA.
Are there any regulations on grass height, density etc?