Fire crews were sent to the Buntingsdale estate near Market Drayton where a small fire in a derelict RAF building had been reported on Sunday afternoon, at about 2.20pm.
They extinguished one fire and found evidence of another, which had burned itself out, and it is believed that both were set deliberately.
The Buntingsdale estate was purchased for the RAF in 1936, and it was used as a base until the mid-1970s.
A statement from the Market Drayton fire team said: "The rescue pumps from Market Drayton and Hodnet, together with an operations officer from headquarters, were all mobilised to a report of a building on fire at Buntingsdale near Market Drayton.
"On arrival the crew found a small fire had been started within a derelict RAF building on the Buntingsdale estate.
"The fire was quickly extinguished by the crew using a high pressure hose reel jet.
"Sadly we can confirm that this fire, along with another that was found to have burnt itself out, had both been started deliberately by persons unknown.
"Our colleagues from West Mercia Police have been informed of this incident and will be carrying out investigations in the area.
"We would like to warn anyone that has been entering this derelict building that there is asbestos present in the building, which can be extremely hazardous to a person's health if loose fibres are breathed in."
Information on crime can be reported to West Mercia Police on the 101 phone number.