The French firm said it was a precautionary measure after finding a defect, in June, in one of the boilers at Heysham 1.
The problem was first detected during a routine boiler inspection, which led to one of the station's two nuclear reactors being shut down.
All four reactors at the stations will be shut as they are of similar design.
The company said all the boilers associated with the two nuclear reactors at Heysham 1, and with the two nuclear reactors at Hartlepool, would be inspected to make sure they were safe.
"Until the results of the further inspections are known it is not possible to advise exact return to service dates for these four reactors, however, an initial estimate is that these investigations will take around eight weeks," said EDF.
"EDF Energy's other nuclear power stations are not affected by this issue as they are of a different design."
The company, owned by the French government, owns and runs other nuclear power stations in the UK: Hunterston and Torness in Scotland, Heysham 2 in Lancashire, Dungeness B in Kent, Hinkley Point B in Somerset and Sizewell B in Suffolk.
The National Grid said the shut-downs would have no effect on the UK's supply of electricity which it said was "fine", helped by low seasonal demand at this time of year.
"We have many generation sources to call on and demand is low at this time of the year," said a spokeswoman.