Kurt Zouma's brother, Yoan, has been banned by Dagenham and Redbridge following his role in the video that showed the West Ham player kicking his cat.
A club statement said: "The Club would like to give a further update on its player, Yoan Zouma.
"Yoan was this week contacted by the RSPCA to assist in their investigation and is fully cooperating with them.
"However, Dagenham & Redbridge FC would again like to reiterate that it condemns any form of cruelty towards animals and fully understands the reaction of many of its supporters.
"The Club has therefore decided that until the RSPCA has completed its investigations, Yoan will not play for Dagenham & Redbridge in any competitive match.
"Any further action deemed necessary to be taken will be made at the conclusion of the RSPCA investigation."
Kurt Zouma has been fined £250,000 and seen had his cats taken away from him by the RSPCA after the footage went viral.
A statement from the animal welfare charity on Wednesday read: "Two cats are now in RSPCA care. Our priority is and has always been the well-being of these cats.
"The cats have been taken for a check-up at the vets and will remain in our care while the investigation continues.
"We're grateful to everyone who expressed their concern for these cats.
"We were dealing with this issue before the video went viral online and are leading the investigation. We continue to investigate so we cannot comment further at this time."
West Ham have copped heavy criticism after they chose to play Kurt Zouma in Tuesday's win over Watford.
The club have condemned his actions and will be dealing with the matter internally, but David Moyes maintained his job was to pick the best XI available.
He said: "The club will sort the other side of it out and I will look after the football side.
"My feeling was Kurt has apologised and I understand that a lot of people will not just accept an apology I understand that.
"But to me, he came out and he said that very honestly and as I said before I had to do my job then and that was to pick the best team I possibly could."
