The pets "exhibited symptoms of sudden collapse, fitting, widespread twitching and general unsteadiness" the firm said, after consuming the biscuits from their range aimed at senior and neutered cats.
The level of thiamine (vitamin B1) in the cat food listed was much lower than the recipe specified.
Pets at Home said customers would be given a full refund.
"An investigation has revealed that, in the four affected products, the level of thiamine (vitamin B1) was much lower than we had specified," the company said in a statement.
It added that the symptoms displayed by the three cats identified were "not the classic symptoms of thiamine deficiency".Image copyright Pets at Home Image caption Four products in the AVA range are being recalled
The AVA range of cat food is sold exclusively at Pets at Home.
The Food Standards Agency, which is also responsible for pet food labelling, said a notification had been sent to vets to alert them to "the atypical symptoms potential for thiamine deficiency".
The company advised customers to dispose of the contents and return the packaging to Pets at Home stores for a refund.