The incident started at 5.15pm when officers received a 999 call to say the canine was in difficulty in the water.
The pet was taken to safety before coastguard officers arrived.
But 25 minutes later they were asked to attend the scene again when a 46-year-old man was reported to have slipped and hurt his leg while in the mud trying to reach the dog.
The victim was taken to Medway Maritime Hospital.