Any process that stops, prevents, or reduces the rate of production of a cytokine.

GO:0042036

GO:0050710

down-regulation of cytokine production

downregulation of cytokine production

negative regulation of cytokine biosynthesis

down regulation of cytokine biosynthetic process

negative regulation of cytokine formation

down regulation of cytokine production

negative regulation of cytokine anabolism

down-regulation of cytokine biosynthetic process

downregulation of cytokine biosynthetic process

negative regulation of cytokine synthesis

negative regulation of cytokine secretion

negative regulation of cytokine biosynthetic process

inhibition of cytokine biosynthetic process

inhibition of cytokine production

biological_process

GO:0001818