McGovern, who wrote shows including The Street and Cracker, recently criticised the "tongue-in-cheek" approach to drama and complained that programmes do not take themselves seriously enough.
McGovern also singled out Doctor Who and Moffat, who writes and produces the series, responded to the remarks on Twitter.
"The tragedy is - no the irony - I DO take Doctor Who seriously," he wrote. "That IS me being serious. Hmm. Just lost the argument, haven't I?"
Meanwhile, The Daily Telegraph reports that Ashes To Ashes scribe Matthew Graham also used Twitter to respond to McGovern's complaints.
"Jimmy accusing Doctor Who of irrelevance," he said. "Perhaps the Doctor should rape all of his companions and turn the TARDIS into a crack den.
"Jimmy - some dramas are about northern people raping their sisters because of the legacy of Thatcher's government. Some dramas are about eccentric time travellers whisking their accomplices off on magical adventures. Some dramas gently and delightfully explore the social morays of the classes in 20th century England. Some dramas brilliantly and compellingly examine the interconnecting lives of residents in a single street."
Graham added: "Jimmy, you are a compelling, humane, acerbic and brilliantly relevant writer. One of our very best. But when you grumble about good shows that entertain millions and ask for the spectrum to be reduced you sound like the enemy of creativity. Worry about your own work and keep your nose out of other people's."
McGovern's new drama Accused begins on November 15 at 9pm on BBC One.