Mr Trump said health had now become "an issue" in the election campaign.
Mrs Clinton was taken ill on Sunday at a 9/11 memorial ceremony and cancelled a campaign trip to California.
She will also be releasing new medical records to help ease concerns about her health, a campaign spokesman said.
"There's no other undisclosed condition. The pneumonia is the extent of it," Brian Fallon told MSNBC.
He said she would probably resume campaigning in the next few days.
Mrs Clinton said on Twitter she was "anxious" to return to the trail.