Zalatoris pulled out before the start of Thursday's round with an undisclosed injury. Na completed the first nine holes of play at 4-over 40 before withdrawing because of an illness, Augusta National Golf Club announced.
Zalatoris, who is ranked eighth in the world, has been battling a back injury for the past several months. He was forced to pull out of the FedEx Cup playoffs after injuring his back in the second round of the BMW Championship in August, a week after he picked up his first PGA Tour victory in a playoff at the FedEx St. Jude Championship. He missed the season-ending Tour Championship.
Zalatoris, 26, who finished in the top 10 in three of four majors last season, returned to action at the Sentry Tournament of Champions in January. He finished fourth at the Genesis in February. Na, who joined the LIV Golf Tour last June, was making his 12th appearance in the tournament before withdrawing. He made a double bogey on the first hole. After making a birdie on the second, he had bogeys on three of the next four holes.
Na went off in the first group with 2003 Masters champion Mike Weir, who was 1 under at the turn. Weir finished the round as a single player.
"I can't remember the last time I played as a single," Weir said after the round. "I'm sure at some point in my career I probably did, but I am struggling to find my memory bank where it was. So that was a strange back nine."
Weir ended up carding an even-par 72. Weir, the first Canadian man to win a major, made the cut in only two of his past 12 starts in the tournament.
Weir said Na informed him at the turn that he was pulling out of the tournament.
"Right there on 10 tee," Weir said. "But he said earlier he wasn't feeling well. So I'm not sure what's happening, but he told me earlier he wasn't feeling well."
LIV Golf CEO and commissioner Greg Norman told The Telegraph of London that if one of the 18 players from LIV Golf competing in the Masters wins a green jacket, the rest would be there Sunday to celebrate with him.
"If one of them wins then the other 17 will hang around and be there to congratulate him around the 18th green," Norman said. "Could you imagine what a scene that would be, all these players hugging the winner. You only see things like that in the Ryder Cup, although it's happening in our events more and more."
Na, 37, has had five victories during his PGA Tour career and made nearly $38 million in on-course earnings.