A spokesman for his Wisebuddah company said there had been no complications and that the 55-year-old hoped to be back at work before the end of 2016.
The news came to light through an automated email response Goodier set up that referred to his absence.
"I am away from work for a time recovering from a stroke and so not seeing email every day," it reads.
Goodier was last heard on the BBC filling in for Radio 2 breakfast presenter Chris Evans on 24 and 25 October.
The former Radio 1 DJ was also heard presenting Radio 2's Pick of the Pops programme earlier this year, following Tony Blackburn's temporary departure.
"At the beginning of November Mark Goodier suffered a stroke and was taken directly to UCH [University College Hospital] in central London," a statement from his production company said.
"He was kept in for a short period and then returned to his home where he is currently recuperating.
"He is receiving excellent medical attention, and recovering very well indeed. He expects to be able to return to work before the end of December."
News of Goodier's condition prompted several of his radio colleagues to send messages of support.
Jeremy Vine said he was sending his friend "love and best wishes", while Sara Cox advised the "radio legend & all round lovely man" to "rest up & get better".
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DJ Mark Goodier is said to be "recovering quite well" after having a stroke at the beginning of November.