Johnson officially pulled out of this week's tournament at Waialae on Monday.
His agent, David Winkle, said in an e-mail that he had some personal matters to attend to at home in South Carolina.
Gulbis was seen following Johnson in the third round last week at Kapalua. She later told golf.com that they were dating, although Johnson has declined to confirm it.
Both have the same sponsor and Butch Harmon as a swing coach. They competed together in the Three-Tour Challenge last year.