Jason Day, 27, who suffers with the condition for several years, needed treatment for a few minutes after his fall.
The Australian regained his footing and missed a putt for par on the ninth hole – his 18th – before succeeding from four feet for a bogey to leave him on two under.
Medical staff had to help Jason Day walk over to sign his scorecard but he said he plans to play on in the tournament.
Jason Day’s agent Bud Martin said: “Jason was diagnosed to have suffered from Benign Positional Vertigo. He is resting comfortably.
“His condition is being monitored closely and he is hopeful he will be able to compete this weekend in the final rounds of the US Open. He wants to thank all who treated him the fans and friends who have reached out to him and his family.”
Playing partner Justin Rose, who shot a level-par 70 to stand at two over, said: “At first I thought he might’ve just rolled his ankle but then when I saw his caddie with a towel round him, I realised it was something else.
“I knew he’d been having some health issues recently and then that’s when your mind starts racing a little bit.”
Vertigo caused world No 10 Jason Day to withdraw from the World Golf Championship in Ohio in 2014 and last month’s Byron Nelson Championship.
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