The fire swept through the 20 metre by 20 metre building in Higher Heath.
Fire crews from Prees and Whitchurch were called to the scene and spent more than an hour tackling the fire, which happened shortly after 2pm on Saturday.
A statement on behalf of Whitchurch Fire Station said: “We were mobilised with our colleagues from Prees to reports of a shed fire in Higher Heath.
“Once in attendance Prees committed two firefighters in breathing apparatus.
“We then put two teams in breathing apparatus from our crew to extinguish the digger and straw that was alight.
“Once the fire was out, crews then had assistance with another digger to pull the straw out to make it easier for us to ensure it was extinguished.
“Good teamwork by both crews to get the incident under control.”