Around 20 firefighters tackled the blaze at The Village Store, Main Street, Addingham, near Ilkley, after they were alerted at 1.34am yesterday.
The blaze followed another fire at the property which is also being treated as suspicious and which happened some time overnight between Monday and the next day.
Detective Inspector John Mountain, of Airedale and North Bradford CID, said: “The two incidents are clearly linked and the second arson attack has subjected the building to serious fire damage.
“We are making good progress with initial lines of enquiry and will be working closely with colleagues from the fire service over the coming days.”
A man, who suffered smoke inhalation, was checked by paramedics at the scene following the latest blaze.
The fire left the shop badly damaged after it swept through the roof of the one-storey building.
The ground floor of an adjoining three-storey property, which is believed to have been empty, was also severely damaged.
Police and fire service investigators remained at the scene yesterday and were conducting “extensive” enquiries in Addingham.
The first blaze which was reported on Tuesday followed a burglary at the premises and is believed to have started in an upstairs room, although it did not spread and caused little damage.
Anyone with information is urged to contact DS Steve Wedge at Airedale and North Bradford CID on 0845 6060606 or CrimeStoppers on 0800 555 111.