"I am being well cared for by the great folk at Wellington hospital," he wrote.
"Keep an eye on those nearest and dearest to you. I'll be back soon."
In an earlier tweet, Plunket, 57, had remarked on how Wellington Hospital seemed to be functioning.
"Strange to have gone from talking about a stressed health system to being in it in a couple of hours," he said.
"Wellington Hospital A & E actually as calm and efficient as I've ever seen it. I'll update later but nothing too serious."
Several listeners sent the radio host their well wishes on social media, urging him to recover quickly.
Plunket started The Platform last year after leaving Magic Talk.
He is a former host of RNZ's Morning Report and has worked as a TV reporter.