The event, held at ESPN's Wide World of Sports outside of Orlando, Florida, marked a return to the league following the suspension of sports in the U.S. in March because of the coronavirus pandemic.
Toronto's match with D.C. United had originally been scheduled for Friday, before it was pushed back to Sunday.
"Major League Soccer announced that today's D.C. United vs. Toronto FC match has been postponed and will be rescheduled," a league statement read. "MLS will announce details later today for the rescheduled match.
"Under the league's health and safety protocols, clubs are tested the day before each match. The results of yesterday's tests for D.C. United and Toronto FC produced an initial unconfirmed positive COVID-19 case for one player and an inconclusive test for another player.
"Because of the arrival time of the clubs in Orlando, the league's protocol called for retesting both teams this morning and to await the results of those tests prior to playing the match.
"Major League Soccer will continue to prioritize the health and safety of all participants of the MLS is Back Tournament in making these decisions."
The tournament has been dogged with issues since FC Dallas pulled out because of a high number of positive COVID-19 tests, before Nashville SC followed suit. Sporting Kansas City also confirmed it had a positive test on Friday, but it is scheduled to play its tournament opener on Sunday evening against Minnesota.
MLS deputy commissioner Mark Abbott stressed there is still confidence that the tournament can proceed.
"The most prudent call was to postpone the match," Abbott said in a conference call early Sunday. "We believe the tournament can be carried out safely. In case it isn't, we'd make a decision."
Six games have been completed in the tournament, in which the points from the group stage count toward the regular-season standings. The opening game saw Orlando City earn a 2-1 victory over Inter Miami CF on Wednesday, with the final scheduled for Aug. 11.
Information from ESPN reporter Tom Marshall was used in this report.