Cat charity Celia Hammond Animal Trust said it was called by the Forest Gate shop owner after he heard the cats crying from the back of a machine.
The device was dismantled and the kittens were reunited with their mother who was found outside the shop.
Charity head Celia Hammond said they "needed some intensive care" but were being looked after in a foster home.
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Four kittens are recovering after they were born inside a tumble dryer in an east London dry-cleaners.