The devices, which are used to store vital data on heart patients, were taken from the hospital's ECG department.
A spokesman for the hospital said the software on the computers was unique and contained essential information on defibrillator implants.
But reports that up to 400 heart patients would be affected by the theft were denied. The figure was "fewer than 10", according to the spokesman.
Police have appealed for information on the theft and the return of the computers.
The laptops were taken from the hospital between Monday morning and Tuesday lunchtime.
Case information
Detective Constable Graham McKellar said: "It is obviously of prime importance that the software from these computers is returned to the hospital immediately.
"I am appealing to anyone who may have either knowledge of the theft or indeed as to the whereabouts of the computers or if anyone is offered the opportunity to buy a laptop computer to contact me as soon as possible."
The data contains information on how many attacks each patient has had, what type of operations they have gone through, and at what voltage each defibrillator has to be set.
Defibrillator boxes deliver several hundred volts of electric shock to restart a patient's heart.
They cost £20,000 each, weigh half a pound and take a major operation to install.
The lifesaving machines cannot function properly without the laptops and the software they contain.
A hospital spokesman said it is thought only a small number of patients will be affected.