Spaniard Rahm had fired a sensational 64 on Saturday to establish a six-shot advantage at the top of the leaderboard before being informed at the end of his third round that he had returned a positive test.
Under PGA Tour protocol, any player who tests positive for Covid-19 must withdraw from the respective tournament.
The defending champion had been undergoing daily tests after being told on Monday that he had come into close contact with someone who had tested positive.
But while each of his previous tests had come back negative, his latest one was positive and he must now isolate until June 15.
A statement on the PGA Tour’s website read: “On the evening Monday, May 31, the PGA Tour notified Jon Rahm that he was subject to contact-tracing protocols, as he had come in close contact with a person who was Covid positive.
“Per the Tour’s Covid Health & Safety Plan, Rahm was given the option to remain in the competition and enter our tracing protocol, which includes daily testing and restricted access to indoor facilities. Rahm has remained asymptomatic.
“Rahm has tested negative every day, but his most recent test – which was performed after the conclusion of his second round (rain delayed) and before the start of his third round – returned positive at approximately 4.20pm (local time) while Rahm was on the golf course.
“The PGA TOUR’s medical adviser requested a confirmatory test on the original sample, which came back at 6.05pm, and was also positive.
“The PGA Tour’s medical adviser notified Rahm immediately upon completion of his round, and under Tour protocols, he will be withdrawn from the competition.
“Rahm is now in isolation, and in accordance with CDC guidelines, he will need to remain in isolation through Tuesday, June 15.”
American pair Collin Morikawa and Patrick Cantlay now lead the tournament on 12 under par.
Morikawa bounced back from a lacklustre Friday to card a six under 66 on Saturday, while Cantlay continued his consistent run with a four under 68.
A late double bogey forced Ireland’s Shane Lowry to settle for an even 72 which dropped him back to equal-10th.
Northern Ireland’s Rory McIlroy and England’s Danny Willett are both one under with a share of 22nd place, while the Scottish duo of Russell Knox and Martin Laird are well back on four over for the tournament.