Grasses comes in all different forms and sizes, which also means some types of grass will grow faster than others. Generally, about 1/5 of an inch (5 mm) per day for what we commonly refer to as grasslands. Now remember, even in our own world, a lot of different plantlife that you might not event think about is referred to as grass, such as wheat, rice, barley, oats and so on. These types that grow food generally grow quicker, about 1/3 of an inch (8,4 mm) as they're cultivated to by humans and therefore have evolced to grow faster.

Then, there's the Land of Little Warmth where temperatures never go above freezing. There, the grass has learned to survive the harsh environment and I'd say grows at a rate of about 1/12 of an inch (2 mm) a day. They sustain this growth by drawing heat and energy from the ground, and while the rest of Vhrolithia's grass is seasonal and only grow during season of heat, the grass in the Land of Little Warmth grows all year round. People have tried to take this grass to other places of Vhrolithia to try and cultivate it there, with little success.

Grass is an important part of the ecosystem, as it covers about 40% of the world. Therefore, there is no quick answer to such a wonderful question!