Mr Trump said health had now become "an issue" in the election campaign.
It will be recalled that 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 has said.
"There's no other undisclosed condition. The pneumonia is the extent of it," Brian Fallon said. He said she would probably resume campaigning in the next few days.