The typical rule of thumb in forestry is that one cubic meter of wood emits (roughly) one tonne of carbon dioxide. The unit of interest in forestry is the volume of wood in the forest. Thus, what you're essentially asking is: how many cubic meters of wood does one hectare of forest have?
This, of course, varies hugely. Forests in warm regions reach a higher density than boreal forests.
Also, you should take into account that lots of forests are managed for maximum productivity. This means the forest won't ever be let to reach its steady-state natural density, because then the growth slows down and the forest becomes uneconomical.
I'll provide an answer for one country: Finland. According to a source, Finland's forests have 2400 million cubic meters of wood per 22.8 million hectares. This means 105 cubic meters of wood per hectare.
So, if the forest fire hits an average forest in Finland, it will release 105 tonnes of carbon dioxide per hectare. Very young forests with practically no trees won't burn (0 tonnes of carbon dioxide per hectare), and old forests ready for renewal will release twice the average, i.e. 210 tonnes of carbon dioxide per hectare.
Edit: the source apparently considers only growing stock, i.e. wood that is above the ground and is usable for commercial purposes. There may be some other biomass as well that will burn. So, treat the 105 tonnes of carbon dioxide per hectare (average forest) or 210 tonnes of carbon dioxide per hectare (old forest) as a lower bound. I still believe the 367 tonnes of carbon dioxide per hectare from Tim's answer is a bit too high for boreal taiga forest.