The force said it had recovered a bladed weapon from the scene, and was not looking for anyone else in connection with the incident at the Sikh place of worship.
Det Supt Ian Dyball said it was being treated as an “isolated incident”.
“Patrols will remain in the area for reassurance and we thank the community for their ongoing support and assistance.”
Officers remained outside the building on Friday morning while inquiries were ongoing.
Gravesham MP Dr Lauren Sullivan said she was “shocked and saddened” by the incident and thanked the emergency services for their “swift” response.
“My thoughts are with those hurt, their family, and the community,” she wrote on X, external.
