'A tournament without Mr. Woods would send a powerful message that discrimination isn't good for the golfing business,' the editorial said.
Augusta National declined comment.
In interviews this month, Augusta National chairman Hootie Johnson was adamant that a woman would not be among the 300 members at Augusta by the start of the Masters in April.
Johnson's comments were the first on the subject since he criticized Martha Burk and the National Council of Women's Organizations for trying to coerce change at the golf course.
The Times said that if Augusta National 'can brazenly discriminate against women, that means others can choose not to support Mr. Johnson's golfing fraternity. That includes more enlightened members of the club, CBS Sports, which televises the Masters, and the players, especially Tiger Woods.'
The editorial said Sanford I. Weill, the chief executive of Citigroup, and Kenneth Chenault, chairman of American Express, should 'lead the way' for other prominent members and resign from the club.
Weill and Chenault have said Augusta National should admit female members. A spokeswoman for American Express refused comment, and a telephone message left for Weill at Citigroup was not returned.
Woods was headed to this week's Dunlop Phoenix tournament in Japan and not immediately available for comment.
Woods has said he would like to see a female member at Augusta National, but that the club had a right to set up its membership however it wanted.
'CBS will broadcast the Masters in April,' CBS Sports VP LeslieAnne Wade said, declining further comment.
The network has had a series of one-year deals since 1956 to televise the Masters, the highest-rated golf tournament.