Jennie Formby accused Mr Watson of behaving in a “completely unacceptable” manner.
She said his approach would “undermine” and “pollute” the existing system of dealing with complaints.
Mr Watson had emailed Labour MPs and peers to say he would be “logging and monitoring” all complaints of antisemitic abuse and bullying.
He asked then to inform him of any complaints of antisemitism so he could ensure they were shared with party leader Jeremy Corbyn and other top figures.
In a letter to Mr Watson, which was forwarded to all Labour MPs and peers, Ms Formby wrote: ”It is absolutely inappropriate for you to set up a vague parallel complaints monitoring system.”
Ms Formby said it was “completely unacceptable” for Mr Watson to receive data relating to such complaints.
The general secretary added: “Furthermore, you will undermine the work that my staff and I are doing and will confuse and pollute the existing formal process, compromising it and slowing it down.”
Ms Formby asked Labour parliamentarians not to send complaints to Mr Watson “or any other unauthorised individual”.
Mr Watson hit back at the remarks as he stood by his decision to intervene.
He said: “The constant concern of those complaining about antisemitism in our party is that there is no transparency about the process.
“This opacity and delay in processing complaints has led to a complete loss of trust.
“Too often those who have suffered antisemitic abuse have not heard anything about the outcome of their complaint.
“It is my responsibility as deputy leader of the Labour Party to ensure people have confidence in our complaints system and our ability to deal transparently with the scourge of antisemitism.
“I will continue to do everything I can to achieve that.”
Meanwhile, Ms Formby has been urged to investigate Diane Abbott’s local constituency party after it called for an immediate start to processes which could see MPs who speak out on antisemitism face deselection.
The motion passed by Hackney North and Stoke Newington Constituency Labour Party hit out at claims of “institutional antisemitism” spread by “the media” and the “right wing of the Parliamentary Labour Party”.
It called on Labour’s ruling National Executive Committee (NEC) to immediately implement trigger ballot procedures in all constituencies in order to allow members to decide on the future of their MPs.
“It is unacceptable to allow our representatives to slander the party and its members whilst we put them into office,” the motion said.
A Labour Party spokesperson said: “We completely reject claims of institutional antisemitism.
“Antisemitism complaints received since April 2018 relate to about 0.1 per cent of our membership, but one antisemite in our party is one too many.
“We are determined to tackle antisemitism and root it out of our party once and for all.”
Additional reporting by Press Association
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies