All eligible asylum-seekers are being required to test negative for the coronavirus before entering the U.S.
The president is holding a campaign event in Winston-Salem.
The president tweeted that he did not visit the hospital for "mini-strokes," blaming "FAKE NEWS" for the rumor – although no news outlet reported that.
The university was scheduled to host the second of three debates between Trump and Biden this fall.
The executive order also applies to plants that have already closed, which will have to re-open with healthy workers.
He has not had "prolonged close contact with any known confirmed" coronavirus patients, the White House said.
