Radio 1 Breakfast Show host Grimshaw said that the Take That star is "not relevant" to his younger listeners.
"Brainless @grimmers @R1Breakfast claims @robbiewilliams is too old & irrelevant for today's teenagers! Some advice.. Stop being a total nob," said Magic FM veteran DJ Dr Fox on Twitter.
"Scary how many people seem to agree with my thought re@grimmers being a #totalnob over his @robbiewilliams comments! It's true though."
He continued: "While I'm having a rant, much as like @onedirection for what they are, if they're the new saviours of @bbcr1 can I have my license fee back?
"Of course I'm not the voice of Today's youth-or trying to be-but @grimmers comments are purely to get a headline."
Fox added to RadioToday: "I'm not the voice of youth but Radio 1 are crazy for saying they're not playing his new song. He'll still be popular when One Direction have split up.
"I know [controller of Radio 1] Ben Cooper - he used to produce my Drive show on Magic - but he needs to work out if Radio 1 is a pop station or not."
He added: "I don't know Nick - I'm sure he's a nice guy but it will be interesting to see how long he lasts now his honeymoon period is over."
Williams has said that he does not mind about Grimshaw's comments, but added that the station should not play Madonna or Coldplay records either if they are only trying to appeal to young listeners.