Gareth Southgate's squad had been training at the 3,300-capacity stadium on Friday around three hours before the blaze started.
The fire, which caused thick black smoke, appeared to take place in the broadcast gantry in between the two dugouts.
After fire crews dealt with the incident, a video assistant referee (VAR) monitor and one dugout looked to be damaged, while there was also a burnt area of the playing surface towards the touchline.
Initial reports have suggested the fixture is not in doubt, but UEFA must decide if it can go ahead at the original venue.
There must be a back-up venue in place for all qualifying matches, per UEFA rules.